£EPA
            United States
            Environmental Protection
            Agency
            Air And Radiation
            (6603J)
PB94-205804
EPA402-R-94-012
June 1994
A Technical Guide To
Ground-Water Model Selection
At Sites Contaminated With
Radioactive Substances

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                                                PB 94-205804
                                             EPA402-R-94-012
                                                   June 1994
        A TECHNICAL GUIDE TO
GROUND-WATER MODEL SELECTION
   AT SITES CONTAMINATED WITH
      RADIOACTIVE SUBSTANCES
               A Cooperative Effort By
           Office of Radiation and Indoor Air
       Office of Solid Waste and Emergency Response
          U.S. Environmental Protection Agency
               Washington, D.C. 20460

           Office of Environmental Restoration
              U.S. Department of Energy
               Washington, D.C. 20585

      Office of Nuclear Material Safety and Safeguards
            Nuclear Regulatory Commission
               Washington, D.C. 20555

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                                      PREFACE
A joint program is underway between the EPA Offices of Radiation and Indoor Air (ORIA) and
Solid Waste and Emergency Response (OSWER), the DOE Office of Environmental Restoration
and Waste Management (EM), and the NRC Office of Nuclear Material Safety and Safeguards
(NMSS). The purpose of the program is to promote the appropriate and consistent use of
mathematical models in the remediation and restoration process at sites containing, or
contaminated with, radioactive materials.  This report is one of a series of reports designed to
accomplish this objective. Other reports completed under this program have identified the models
in actual use at NPL sites and facilities licensed under RCRA, and at DOE sites and NRC sites
undergoing decontamination and decommissioning (D&D), as well as the role of modeling and
modeling needs in each phase of the remedial investigation. This report specifically addresses the
selection of ground-water flow and contaminant transport models and is intended to be used by
hydrogeologists and geoscientists responsibile for identifying and selecting ground-water flow and
contaminant transport models for use at sites containing radioactive materials.

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                              ACKNOWLEDGMENTS


This project is coordinated by the Office of Radiation and Indoor Air, U.S. Environmental
Protection Agency, Washington, D.C., and jointly funded by the following organizations:

EPA Office of Radiation and Indoor Air (ORIA)
EPA Office of Solid Waste and Emergency Response (OSWER)
DOE Office of Environmental Restoration and Waste Management (EM)
NRC Office of Nuclear Material Safety and Safeguards (NMSS)

The project Steering Committee for this effort includes:

EPA

Beverly Irla, EPA/ORIA Project Officer
Ronald Wilhelm, EPA/ORIA
Kung-Wei Yeh,  EPA/ORIA
Loren Henning,  EPA/OSWER

DOE

Paul Beam, DOE/EM

NRC

Harvey Spiro, NRC/NMSS

Consultants and Contractors

John Mauro, S. Cohen & Associates, Inc.
David Back, HydroGeoLogic, Inc.*
Paul Moskowitz, Brookhaven National Laboratory
Richard Pardi, Brookhaven National Laboratory
James Rumbaugh, Geraghty & Miller, Inc.

  *principal author

We acknowledge the technical support and cooperation provided by these organizations and
individuals. We also thank all reviewers for their valuable observations and comments.

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                                      CONTENTS

                                                                                   Page

Preface 	 i

Acknowledgments	ii

Summary	S-l

1  Introduction	  1-1
   1.1 Background - Purpose and Scope of the Joint EPA/DOE/NRC Program  	  1-1
   1.2 Purpose and Scope of this Report  	  1-3
   1.3 Principal Sources of Information  	  1-4
   1.4 Key Terms	  1-4
   1.5 Organization of the Report	  1-5

2  Modeling Decisions Facing the Site Remediation Manager	2-1
   2.1 Is Ground  Water a Potentially Important Exposure Pathway?	2-1
   2.2 Reasons for Modeling 	2-3
   2.3 Planning for Modeling	2-3
          2.3.1   Identifying Modeling Needs	2-3
          2.3.2  Sources of Assistance  	2-7
                 2.3.2.1 Branches and Divisions Within Agencies  	2-7
                 2.3.2.2 Electronic Media	2-7

3  Constructing and Refining the Conceptual Model of the Site  	3-1
   3.1 Basic Questions that Will Need to be Answered	3-2
   3.2 Components of the Conceptual Model for the Ground-water Pathways 	3-2
          3.2.1   Contaminant/Waste Characteristics 	3-2
          3.2.2  Environmental Characteristics	3-3
          3.2.3   Land Use and Demography	3-5

4  Code Selection - Recognizing Important Model Capabilities	4-1
   4.1 Introduction	4-1
   4.2 General Considerations - Code Selection During Each Phase in the Remedial Process  4-1
          4.2.1   Scoping	4-3
                 4.2.1.1 Conservative Approximations 	4-3
                 4.2.1.2 Steady-State Solutions	4-5
                 4.2.1.3 Restricted Dimensionality  	4-5
                 4.2.1.4 Uncomplicated Boundary and Uniform Initial Conditions	4-7
                 4.2.1.5 Simplified Flow and Transport Processes	4-8
                 4.2.1.6 Uniform Properties 	4-8
                                           in

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                                CONTENTS (Continued)

                                                                                    Page

          4.2.2  Site Characterization	4-9
                 4.2.2.1 Site-Specific Approximations	4-10
                 4.2.2.2 Steady-State Flow/Transient Transport  	4-10
                 4.2.2.3 Multi-Dimensional	4-11
                 4.2.2.4 Constant Boundary and Non-uniform Initial Conditions	4-12
                 4.2.2.5 Complex Flow and Transport Processes	4-13
                 4.2.2.6 System Heterogeneity  	4-14
          4.2.3  Remedial Phase	4-14
                 4.2.3.1 Remedial Action Specific	4-15
                 4.2.3.2 Transient Solutions  	4-18
                 4.2.3.3 Multi-Dimensional	4-18
                 4.2.3.4 Transient Boundary and Non-Uniform Initial Conditions 	4-18
                 4.2.3.5 Specialized Flow and Transport Processes	4-19
                 4.2.3.6 System Heterogeneity  	4-20
       4.3     Specific Considerations	4-20
          4.3.1  Site-Related Characteristics	4-23
                 4.3.1.1 Source Characteristics	4-23
                 4.3.1.2 Aquifer and Soil/Rock Characteristics  	4-27
                 4.3.1.3 Transport and Fate Processes	4-36
                 4.3.1.4 Multiphase Fluid Conditions  	4-41
                 4.3.1.5 Flow Conditions 	4-42
                 4.3.1.6 Time Dependence  	4-43
          4.3.2  Code-Related Characteristics	4-43
                 4.3.2.1 Geometry   	4-44
                 4.3.2.2 Source Code Availability	4-45
                 4.3.2.3 Code Testing and Processing	4-45
                 4.3.2.4 Model Output  	4-47
       4.4     Modeling Dilemmas	4-47

5  The Code Selection Process	5-1
   5.1 Overview of the Code Review and Selection Process	5-1
   5.2 Evaluation Criteria	5-5
          5.2.1  Administrative Data	5-5
          5.2.2  Criteria Based on Phase in the Remedial Process	5-7
          5.2.3  Criteria Based on Waste and Site Characteristics	5-7
          5.2.4  Criteria Based on Code Characteristics  	5-10

References	R-l

Bibliography 	B-l
                                            IV

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                               CONTENTS (Continued)

                                                                                Page

Appendices

   A  Glossary	A-l
   B  Ground-water Modeling Resources  	B-l
   C  Solution Methodology	C-l
   D  Code Attribute Tables 	D-l
   E  Index  	 E-l

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                                       FIGURES

Number                                                                            Page

1-1    Exposure Pathways  	  1-1

3-1    Example Conceptual Model	3-1

4-1    One-Dimensional Representation of Conceptual Model	4-5
4-2    Two-Dimensional Cross-Sectional Representation of Unsaturated Zone in
       Conceptual Model	4-6
4-3    Two-Dimensional Areal Representation of Saturated Zone Conceptual Model	4-6
4-4    Three-Dimensional Representation of Conceptual Model	4-6
4-5    Typical System Boundary Conditions	4-7
4-6    Water Table and Confined Aquifers	4-28
4-7    Perched Water	4-31
4-8    Macropores and Fractures	4-32
4-9    Hydrodynamic Dispersion	4-38
4-10   Matrix Dispersion	4-39

5-1    Code Selection Review Process	5-3
5-2    General Classification of Selection Criteria	5-6
5-3    Physical, Chemical, and Temporal Site-Related Selection Criteria	5-9
5-4    Source Code Availability and History of Use Selection Criteria  	5-11
5-5    Quality Assurance Selection Criteria  	5-12
5-6    Hardware Requirements Selection Criteria	5-17
5-7    Mathematical Solution Methodology Acceptance Criteria	5-18
5-8    Code Output Selection Criteria  	5-19
5-9    Code Dimensionality Selection Criteria  	5-21
                                           VI

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                                       TABLES

Number                                                                          Page

2-1    Matrix of Reasons for Modeling	2-4

4-1    General Modeling Approach as a Function of Project Phase	4-2

4-2    Questions Pertinent to Model Selection 	4-21
4-3    Site-Related Features of Ground-Water Flow and Transport Codes	4-24
4-4    Code-Related Features of Ground-Water Flow and Transport Codes	4-25

5-1    Model Selection Criteria  	5-4
                                          vn

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                                             SUMMARY

          A TECHNICAL GUIDE TO GROUND-WATER MODEL SELECTION
           AT SITES CONTAMINATED WITH RADIOACTIVE SUBSTANCES
S.I INTRODUCTION

A  joint  program  is  underway  between  the
Environmental Protection Agency (EPA) Offices of
Radiation and Indoor Air (ORIA) and Solid Waste and
Emergency Response (OSWER), the Department of
Energy (DOE) Office of Environmental Restoration
and  Waste  Management  (EM),  and  the  Nuclear
Regulatory Commission (NRC)  Office of Nuclear
Material Safety and Safeguards (NMSS). The purpose
of the program is to  promote the appropriate  and
consistent  use  of  mathematical  models  in  the
remediationandrestorationprocess at sites containing,
or contaminated with,  radioactive  materials.  This
report, which is one of a series of reports designed to
accomplish this objective,  specifically addresses the
selection  of  ground-water flow  and  contaminant
transport  models.   It  is  intended  to  be used by
hydrogeologists and geoscientists  responsible  for
identifying and  selecting ground-water flow  and
contaminant  transport models  for  use at  sites
containing or contaminated with radioactive materials.

Previous reports in this series have determined that the
types of  models  and  the processes  that  require
modeling  during the remedial process  depend on a
combination of the following five factors:

    1.   reasons for modeling,
    2.   contaminant/waste characteristics,
    3.   site environmental characteristics,
    4.   site land use and demography, and
    5.   phase of the remedial process.

This report describes and provides a rationale for the
methods   for  selecting  ground-water  flow  and
contaminant transport models and computer codes that
meet the  modeling needs at sites  containing, or
contaminated  with, radioactive  materials.    The
selection process is described  in terms of the  various
site characteristics and processes requiring modeling
and the availability, reliability, and useability of the
computer codes that meet the modeling needs.

Though this report is limited to a discussion of the
model selection process, the proper application of the
selected codes is as important, if not more important,
than code selection. A code, no matter how well suited
to a particular application, could give erroneous and
highly misleading results if used improperly or with
incomplete or erroneous input data.  Conversely, even
a code with very limited capabilities, or a code used at
a site which has not been well characterized, can give
very useful results if used intelligently and with a full
appreciation of the limitations of the code and the
input data.

It was not possible, within the scope of this report, to
address computer code applications, quality control,
and the presentation and interpretation of modeling
results.   Future reports to be prepared  under this
program will address these important topics.

The report is divided into five sections. Following this
introduction,  Section 2 presents an overview  of the
types of ground-water modeling decisions facing the
site remediation manager. This section is designed to
help the site manager and/or earth scientists to
determine the role of, and  need for, modeling in
support of remedial decision making.

Section 3 addresses the construction of a conceptual
model of a site and how it is used in the  initial
planning and scoping phases of a site remediation,
especially as  it  pertains to the selection and use of
ground-water flow and contaminant transport codes.

Section 4 describes the various site characteristics and
ground-water   flow   and  contaminant  transport
processes that may need to be explicitly modeled. The
purpose of this  section is to help the earth scientists
recognize the conditions  under which specific code
features  and capabilities are  needed  to support
remedial decision making during each phase in the site
remediation process.

Section 5 describes the computer  code  review and
evaluation  process for screening  and selecting the
computer codes that are best suited to meet site-specific
modeling needs.
                                                  S-l

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S.2 MODELING QUESTIONS  FACING
    SITE REMEDIATION MANAGER
THE
A review  of current regulations  and  guidelines
pertaining to the remediation of sites on the National
Priorities  List  (NPL)  and  in the  NRC's  Sites
Decommissioning  Management Program (SDMP)
reveals that fate and effects modeling is not explicitly
required.  However, in order to make informed and
defensible remedial decisions, ground-water flow and
contaminant transport modeling can be useful and is
often necessary.

S.2.1   When is Ground-Water Modeling
        Needed?

The  first questions that a site  remediation manager
will need to answer regarding ground-water modeling
include:  Is ground-water modeling needed, and how
will  modeling aid  in the remedial decision making
process?

The  ground-water  pathway may be considered a
potentially  significant exposure pathway if  (1) the
radionuclide  concentrations in  the  ground  water
exceed the levels acceptable to the cognizant regulatory
authorities or (2) the contamination at the site could
eventually cause the radionuclide concentrations  in
ground water to exceed the applicable criteria.  On this
basis, if the measured concentrations of radionuclides
in ground water downgradient from the site,  or  in
leachate at the site, exceed the applicable criteria, and
the ground water in the vicinity of the site is being
used, or has the  potential to be used, as a source  of
drinking water, it is likely that ground-water modeling
will be useful, if not necessary,  in support of remedial
decision making at the site.

The  "applicable  criteria" are ill-defined at this time
because  both NRC  and EPA  are  engaged   in
rulemaking activities intended to define the criteria.
However, in the interim, the drinking-water standards
set forth in  40  CFR  141 should  guide remedial
decision making. For example, 40 CFR 141 has been
cited as  an  applicable or relevant and  appropriate
regulation (ARAR) in establishing the remediation
goals  at  most  of the  approximately  50  sites
contaminated  with radioactive  material that are
currently on the National Priorities List.

At some  sites,  information may not be available
regarding the levels of radionuclide contamination in
ground water or leachate. Alternatively, radionuclide
measurements  may  have  been  made,  but yield
inconclusive  results.  Under these conditions, the
radionuclide concentrations in leachate and ground
water can be estimated  based on knowledge of the
radionuclide concentrations in the soil or the waste at
the site and empirically determined partition factors.
Partition factors relate a given concentration of a
contaminant in the waste or  the soil to that in the
leachate or ground water.

If the product of the radionuclide concentrations in the
waste or  contaminated soil  with  the  appropriate
partition factors results in radionuclide concentrations
in leachate or ground water in excess of the applicable
criteria, it may be concluded that the  radionuclide
concentrations in ground water in the vicinity of the
site could  exceed the applicable criteria. Though it is
not necessarily always the case,  if the  measured or
derived  concentrations of radionuclides  in ground
water exceed the applicable criteria, it is likely  that
ground-water modeling  will  serve a useful role in
support of remedial decision making at the site.

S.2.2   When is Modeling Not Needed or
        Inappropriate?

It  is important  to  be  able  to recognize  the
circumstances  under  which   modeling would be
ineffective and should probably  not be performed.
There are  three general scenarios in which modeling
would be of limited value.  These are:

    1.   Presumptive remedies can be readily
        identified,

    2.   Decision making is based on highly
        conservative assumptions, and/or

    3.   The site is too complex to model
        realistically.

The first case arises in situations where a presumptive
remedy  is apparent; that  is,  where the remedy is
obvious based on regulatory requirements or previous
experience, and there is a high level of assurance that
the site is well understood and the presumptive remedy
will be effective. An example would be conditions that
obviously  require  excavation or  removal  of the
contaminant source.
The second case is based on the  assumption  that
decision making can proceed  based on conservative
estimates of the behavior and impacts of contaminants
at the site rather than detailed modeling. This strategy
                                                   S-2

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could  be   used  in  the  initial  scoping,   site
characterization,  or  remedial  phase   of  the
investigation. For example, a conservative approach
to the risk  assessment would be to assume that the
contaminant  concentrations  at the receptor(s) are
identical to the higher concentrations detected at the
contaminant source.  Thus, the need for modeling to
determine the effects of dilution and attenuation on
contaminant concentrations is removed.

The third case involves sites where modeling would be
helpful in supporting remedial decision making, but
the complexity of the site precludes reliable modeling.
These  complexities could be associated  with the
contaminant source, flow and transport processes, or
characteristics of the wastes  and contaminants.  For
example, the contaminant source may be  so poorly
defined in terms of areal  extent, release history, and
composition that it cannot be reliably defined and little
would be gained from flow and transport modeling.

Complex flow and contaminant  transport  processes
present  another  difficulty  in  that  user-friendly
computer  codes  currently   do  not  exist  that
accommodate a  number  of  these  processes, which
include:  turbulent ground-water flow,   facilitated
transport (e.g., due to the formation of colloids), and
flow and transport through a fractured unsaturated
zone.

The  availability  of computer codes is also an  issue
when characteristics of the contaminants are typified
by complex  geochemical reactions,  such  as  phase
transformations  and non-linear sorption processes.
Currently,  ground-water flow  and  contaminant
transport codes  that provide credible mathematical
descriptions  of  the  more  complex  geochemical
processes have not been developed.  If modeling is not
possible because of the overall  complexity of the site
characteristics, it is common for a greater emphasis to
be placed on empirical  rather than predicted  data.
This may involve establishing long-

term monitoring programs,  which, in effect,  have
objectives similar to those of ground-water modeling.
S.2.3   What Role Will Ground-Water Modeling
        Play in Support of Remedial
        Decision Making?

Once it is determined that the ground-water exposure
pathway is potentially important, ground-water flow
and transport modeling can have a wide range of uses
in support of remedial decision making. The following
are the principal reasons for modeling on a remedial
project. These applications can surface during any
phase of the remedial process. However, some of these
reasons are more likely to occur during specific phases
of a remedial project.

1.  When  it is   not  feasible  to  perform  field
    measurements; i.e.,

     !   Cannot get access to sampling locations
     !   Budget is limited
     !   Time is limited

2.  When there is concern that downgradient locations
    may become  contaminated at some  time  in the
    future;  i.e.,
    i
        When transport times from the source of the
        contamination to potential receptor locations
        are long relative to the period of time the
        source of the contaminant has been present.
        When planning to store or dispose of waste at
        a  specific  location  and  impacts  can  be
        assessed only through the use of models.
3.   When  field data alone  are  not sufficient to
    characterize fully the nature and extent of the
    contamination; i.e.,

    !    When field sampling is limited in space and
        time, and
    !    When field sampling results are ambiguous or
        suspect.

4.   When there is concern that conditions at a site
    may  change, thereby  changing  the  fate  and
    transport of the contaminants; i.e.,

    !    seasonal changes in environmental conditions
    !    severe  weather (e.g., floods)
    !    accidents (e.g., fires)

5.   When there is concern that institutional control at
    the site may be lost  at some time in the future
                                                   S-3

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    resulting in new exposure scenarios, or a change
    in the fate and transport of the contaminants; i.e.,

    !    trespassers
    !    inadvertent intruder (construction/
        agriculture)
    !    human intervention (drilling, excavations,
        mining)

6.   When remedial actions are planned and there is a
    need to predict the effectiveness of alternative
    remedies.

7.   When there is a need to predict the time when the
    concentration of specific contaminants at specific
    locations will decline to acceptable levels (e.g.,
    natural flushing).

8.   When there is concern that at some time in the
    past individuals were exposed to elevated levels of
    contamination and it is desirable to reconstruct the
    doses.

9.   When there is concern that contaminants may be
    present but below  the lower limits of detection.

10. When field measurements reveal the presence of
    some  contaminants,  and  it  is  desirable  to
    determine  if  and  when  other contaminants
    associated with the source may arrive, and at what
    levels.

11. When field measurements reveal the presence of
    contaminants and it is desirable to identify the
    source or sources of the contamination.

12. When there is a need to determine the timing of
    the remedy; i.e., if the remedy is delayed, is there
    a  potential for environmental or public health
    impacts in the future?

13. When there is a need to determine remedial action
    priorities.

14. When demonstrating compliance with regulatory
    requirements.

15. When estimating the benefit  in a cost-benefit
    analysis of alternative  remedies.

16. When performing a  quantitative  dose or risk
    assessment  pertaining  to  the  protection  of
    remediation  workers,  the  public,   and  the
    environment  prior  to,  during,  and  following
    remedial activities.

17. When designing the site characterization program
    (e.g., placement of monitor wells, determining
    data needs) and identifying exposure pathways of
    potential significance.

18. When there is a need to compute or predict the
    concentration distribution in space and time of
    daughter products from the original source of
    radionuclides.

19. When there is a need to quantify the degree of
    uncertainty in the anticipated behavior of the
    radionuclides  in  the  environment  and  the
    associated doses and risks.

20. When  communicating with the public  on the
    potential impacts of the site and the benefits of the
    selected remedy.

S.2.4   What Will the Results of a Modeling
        Exercise Yield?

Once the need for, and role of,  modeling is identified,
it is appropriate to determine or define the form of the
results or output of the modeling exercise. In general,
the results  are expressed as  a  concentration, such as
pCi/L  in ground water at a specific location.  The
derived radionuclide concentrations could also be
expressed as a function of time or as a time-averaged
value.

Some computer codes have the ability to convert the
derived radionuclide concentrations in ground water to
doses  or  risks  to  individuals  exposed  to  the
contaminated  ground  water.    These results  are
generally expressed in units of mrem/yr or lifetime risk
of cancer for the exposed individuals.

Some computer codes can present the results in terms
of cumulative  population impacts.  These results are
generally expressed in terms of person-rems/yr or total
number of cancers induced  per year in the exposed
population.

The specific regulatory requirements that apply to the
remedial program determine  which of these  "end
products"  are  needed.   In general, these  modeling
results are used to assess impacts or compliance with
                                                   S-4

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applicable regulations; however, information regarding
radionuclide  flux and plume  arrival times  and
distributions is also used to support a broad range of
remedial decisions.

These modeling endpoints  must be clearly defined,
since the type of endpoint will help to determine the
type of ground-water flow and contaminant transport
model that will support the  endpoint of interest.  For
example,  a  baseline  risk assessment  at a  site
contaminated with radioactive  material is used in
determining the annual radiation dose to an individual
drinking  water   obtained  from  a  potentially
contaminated well.  The endpoint in this case is the
dose to an individual expressed in units of mrem/yr.
In order to estimate this  dose, it is  necessary to
estimate the average concentration of radionuclides in
the well water over the course of a year. The models,
input parameters, and assumptions  needed to predict
the annual average  radionuclide concentration are
different than those needed to predict the time varying
concentration at a given location. The latter usually
requires much more input data and models capable of
simulating dynamic processes.

S.3 CONSTRUCTING A CONCEPTUAL
        MODEL OF A SITE - THE FIRST STEP
        IN THE MODEL SELECTION
        PROCESS

The  first step in  the  model selection  process is the
construction of a conceptual model of the site.  The
conceptual model depicts  the types  of waste  and
contaminants, where  they are located  (e.g., are  they
currently  only  in the  surficial  soil  or have  they
migrated to the underlying aquifer?), and how they are
being transported offsite (e.g., by runoff, percolation
into  the ground,  and transport  in  ground  water, or
suspension or volatilization into the air and transport
by the prevailing meteorological conditions).   The
conceptual model also attempts to help visualize the
direction and path followed by the contaminants, the
controlling  factors  that   affect  the  contaminant
migration through the subsurface (i.e., hydrogeology,
system boundary  conditions), the actual or potential
locations  of the receptors,  and  the ways  in which
receptors may be exposed, such as direct contact  with
the source, ingestion of contaminated food or water, or
inhalation of airborne contaminants. As information
regarding a site accumulates, the conceptual model is
continually revised and refined.
A mathematical model translates the conceptual model
into a series of equations which simulate the fate and
effects  of the  contaminants  as  depicted  in the
conceptual model at a level  of accuracy that can
support remedial decision making.  A computer code
is simply a tool that is used to solve the equations
which constitute the mathematical  model of the site
and display the  results in a manner  convenient to
support remedial decision making.  Accordingly, code
selection  must begin  with the construction of a
conceptual model of the site.

The components that make up the  initial conceptual
model of the site include:

    1.   the waste/contaminant characteristics,
    2.   the   site  characteristics,   including
        hydrogeology, land use, and demography, and
    3.   the exposure scenarios and pathways.

S.3.1    Waste/Contaminant Characteristics

To the extent feasible, the site conceptual model should
address  the  following   characteristics  of  the
waste/contaminants:

    !    Types and chemical composition of the
        radionuclides

    !    Waste form and containment

    !    Source geometry  (e.g., volume, area, depth,
        homogeneity)

Within  the context of ground-water modeling, these
characteristics are pertinent to modeling the  source
term,  i.e., the  rate  at   which radionuclides  are
mobilized from the source and enter the unsaturated
and saturated zones of a site.

S.3.2    Site Characteristics

The conceptual  model of the site  should begin to
address the complexity of the environmental  and
hydrogeological setting. A complex setting,  such as
complex lithology, a thick unsaturated zone,  and/or
streams or other bodies of water on  site, generally
indicates that the direction and velocity  of ground-
water flow and radionuclide transport at the site cannot
be reliably simulated using simple models.
                                                   S-5

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However, even at complex sites, complex models may
not be  needed.   For example,  if  a conservative
approach is  taken,  where transport through  the
unsaturated zone is assumed to be instantaneous, then
the complex processes  associated with  flow and
transport through the unsaturated zone would not need
to be  modeled.   Such an  approach  would be
appropriate at sites where the remedy is likely to be
removal of the contaminated surface and near-surface
material.

The site conceptual model will also need to identify the
locations where ground water is currently being used,
or may be used in the future, as a private or municipal
water supply. At sites with multiple user locations, an
understanding of ground-water flow  in two or three
dimensions is needed in order to predict realistically
the likelihood that the contaminated plume will be
captured by the wells located at different directions,
distances, and  depths  relative  to  the sources of
contamination.

Simple  ground-water  flow and transport  models
typically  are  limited to estimating the radionuclide
concentration in the plume  centerline down-gradient
from the source.  Accordingly, if it is assumed that the
receptors are located at the plume centerline, a simple
model may be appropriate.  Such an assumption is
often appropriate even if a receptor is not currently
present at the centerline location because the results
are  generally  conservative.    In  addition,  risk
assessments often postulate that a receptor could be
located directly down-gradient of the source at some
time in the future.

The need for complex models increases if there are a
number of water supplies in the vicinity of the source.
Under these  circumstances, it may be necessary to
calculate the  cumulative population doses and risks,
which   require  modeling   the   radionuclide
concentrations  at  a number  of specific receptor
locations. Accordingly, off-centerline modeling which
includes dispersion may be needed.
S.3.3   Exposure Scenarios and Pathways

The  conceptual model of the site will also need to
define the exposure scenarios and pathways at the site.
An exposure scenario pertains to the assumed initial
conditions  or initiating events responsible for  the
transport of the radionuclides and exposure of the
nearby  population.  Depending  on the regulatory
requirements and the phase in the remedial process,
the exposure scenarios that will need to be modeled
can include any one or combination of the following:

    !    The no  action alternative -  Under this
        scenario,  the radiation  doses  and risks to
        members of the public, now and in the future,
        are derived assuming no action is taken to
        remedy the site or protect the  public from
        gaining access to the site.

    !    Trespassers - This scenario postulates that an
        individual trespasses on the site.

    !    Inadvertent  intruder   -  This   scenario
        postulates  that an  individual  establishes
        residence at the site.

    !    Routine  emissions - This scenario  simply
        assesses  offsite doses and risks associated
        with the  normally anticipated releases from
        the site.  (This  concept is similar to the "No
        Action Alternatives," but is used within the
        context of NRC licensed facilities.)

    !    Accidents - This scenario assesses doses and
        risks associated with postulated accidental
        releases from the site.

    !    Alternative remedies - This set of scenarios
        assesses the doses and risks to workers and
        the public associated with the implementation
        of specific remedies  and the  reduction in
        public   doses  and  risks   following
        implementation of the remedy.

The number of scenarios that may be  postulated is
virtually unlimited. Accordingly,  it is necessary to
determine which scenarios reasonably bound what may
in fact occur at the site. The types of scenarios selected
for consideration influence modeling needs because
they  define  the  receptor  locations and exposure
pathways that need to be modeled.

For  each  scenario,  an  individual  or group  of
individuals may be exposed by  a wide variety  of
pathways. The principal pathways include:

    !    External exposure to deposited radionuclides
                                                   S-6

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    !    External exposures to airborne, suspended,
        and resuspended radionuclides

    !    Inhalation exposures to airborne, suspended,
        and resuspended radionuclides

    !    Ingestion of radionuclides in food items and
        drinking water

    !    Ingestion of contaminated soil and sediment

    !    External  exposures  from  immersion  in
        contaminated water

S.4 CODE SELECTION - RECOGNIZING
        IMPORTANT MODEL CAPABILITIES

The greatest difficulty facing the investigator during
the code selection process  is not determining which
codes have  specific  capabilities, but rather which
capabilities are actually required to support remedial
decision  making during each remedial phase at a
specific site.  This section is designed to  help the
remedial manager  recognize the  conditions under
which  specific model features and capabilities are
needed to support remedial decision making.

S.4.1    Code Selection During the Different Phases
        of a Remedial Program

Successful  ground-water  modeling  requires  the
selection of a computer code that is not only consistent
with the site characteristics but also with the modeling
objectives, which are strongly dependent on the phase
of the  remedial  process;  i.e.,  scoping versus  site
characterization  versus  the   selection  and
implementation of a remedy. Table S-l presents an
overview of how the overall approach to modeling a
site differs as a function of the phase of the remedial
process.

The  most  common  code  selection  mistakes  are
selecting codes that are more sophisticated than are
appropriate for the  available data or the level of the
result  desired,   and  the   application  of  a less
sophisticated code that does not account for the flow
and transport processes that dominate the system.
            Table S-l. General Modeling Approach as a Function of Project Phase
Attributes
Accuracy
Temporal Representation of
Flow and Transport Processes
Dimensionality
Boundary and Initial
Conditions
Assumptions Regarding Flow
and Transport Processes
Lithology
Methodology
Data Requirements
Scoping
Conservative
Approximations
Steady-State Flow and
Transport Assumptions
One Dimensional
Uncomplicated
Boundary and Uniform
Initial Conditions
Simplified Flow and
Transport Processes
Homogeneous/Isotropic
Analytical
Limited
Characterization
Site-Specific
Approximations
Steady-State Flow/Transient
Transport Assumptions
1 ,2-Dimensional/Quasi-
3-dimensional
Non-Transient Boundary
and Nonuniform Initial
Conditions
Complex Flow and
Transport Processes
Heterogeneous/Ani so tropic
Semi-Analytical/Numerical
Moderate
Remediation
Remedial Action Specific
Transient Flow and
Transport Assumptions
Fully 3-Dimensional/Quasi-
3-dimensional
Transient Boundary and
Nonuniform Initial
Conditions
Specialized Flow and
Transport Processes
Heterogeneous/Ani so tropic
Numerical
Extensive
                                                  S-7

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For example, a typical question that often arises is:
should three-dimensional codes be used as opposed to
two- or one-dimensional codes?  Inclusion of the third
dimension requires substantially more data than one-
and two- dimensional codes. Similar questions need to
be   considered   which   involve  the   underlying
assumptions in the selection of an approach and the
physical processes which are to be addressed.  If the
modeler is not practical, sophisticated codes are used
too early in the problem analysis.  In  other instances,
the complexity of the modeling is commensurate with
the qualifications of the modeler.

An inexperienced modeler may  take an unacceptably
simplistic  approach.  One  should begin with  the
simplest code appropriate to the problem and progress
toward the more sophisticated codes until the modeling
objectives are achieved.

The remedial process is generally structured in a way
that  is consistent with this philosophy;  i.e., as  the
investigation  proceeds,   additional   data  become
available to support more sophisticated ground-water
modeling.

The data available in the early phases of the remedial
process may  limit the modeling to  one  or two
dimensions. In certain cases, this may be sufficient to
support remedial decision making.  If the modeling
objectives cannot be met  in this manner, additional
data will be needed to support the use of more complex
models.

It is generally in the later phases of the investigation
that sufficient data have been obtained to meet more
ambitious  objectives  through  complex    three-
dimensional modeling.

The necessary degree of sophistication of the modeling
effort can be evaluated in terms of both site-related
issues and objectives, as well as the qualities inherent
in the  computational  methods available for solving
ground-water flow and transport equations.

Modeling  objectives at each stage of the remedial
investigation must be very specific and well defined
early in the  project.   All too  often, modeling is
performed without developing a clear rationale to meet
the  objectives,  and  only after  the  modeling  is
completed are  the  weaknesses  in  the approach
discovered.
The modeling objectives must consider the available
data and the remedial decisions that the model results
are intended  to  support.    The selected modeling
approach should not be driven by the data availability,
but the modeling objectives should be defined in terms
of what can be accomplished with the  available data.
If the modeling objectives demand more sophisticated
models and input data, the necessary data should be
obtained.

A final consideration, true for all phases of the project,
is to select codes that have been accepted by technical
experts and used within a regulatory context.

S.4.2    The Effects of Waste/Contaminant and Site
        Characteristics on  Code Selection

After  the  conceptual model is formulated and  the
modeling   objectives   are   clearly  defined,   the
investigator should have a relatively good idea of the
level of sophistication that the anticipated modeling
will require. It now becomes necessary  to select one or
more  computer  code(s)  that have  the attributes
necessary  to mathematically describe the conceptual
model at the desired level of detail. This step in the
code selection process requires detailed analysis of the
conceptual model to determine the degree to which
specific waste/contaminant  and site  characteristics
need to be explicitly modeled.

The  code  selection process  consists primarily  of
determining which waste/contaminant and site charac-
teristics and flow and transport processes need to be
explicitly modeled in order to achieve the modeling
objectives.   Once these are  determined, the code
selection process becomes simply a matter of identi-
fying the codes that meet the  defined modeling needs.

Table  S-2 lists  code attributes related  to  various
waste/contaminant and site characteristics. This table
illustrates the site-related criteria generally considered
in the identification of candidate computer codes.

The general components of the conceptual model that
need to be considered when  selecting  an appropriate
computer code are the following:

    !    Source Characteristics

    !    Aquifer and Soil/Rock Characteristics
                                                   S-8

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Table S-2. Site-Related Features of Ground-Water Flow and Transport Codes
Section 4. 3. 1.1
Section 4. 3. 1.2
Section 4. 3. 1.3
Section 4. 3. 1.4
Section 4. 3. 1.5
Section 4. 3. 1.6
Source Characteristics
Point Source
Line Source
Areally Distributed Source
Multiple Sources
Specified Concentration
Specified Source Rate
Time-Dependent Release
Aquifer and Soil/Rock Characteristics
Confined Aquifers
Confining Unit(s)
Water-Table Aquifers
Convertible Aquifers
Multiple Aquifers
Homogeneous
Heterogeneous
Isotropic
Anisotropic
Fractures
Macropores
Layered Soils
Fate and Transport Processes
Dispersion
Advection
Matrix Diffusion
Density -Dependent Flow and Transport
Retardation
Non-linear Sorption
Chemical Reactions/Speciation
Single Species First Order Decay
Multi-Species Transport with Chained Decay Reactions
Multiphase Fluid Conditions
Two-Phase Water/NAPL
Two-Phase Water/ Air
Three-Phase Water/NAPL/ Air
Flow Conditions
Fully Saturated
Convertible Aquifers
Variably Saturated/Non-Hysteretic
Variably Saturated/Hysteretic
Time Dependence
Steady-State
Transient
Fate and Transport Processes
Multiphase Fluid Conditions
                                     S-9

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Each of these topics is presented as a major heading in
Table S-2.  These broad subjects are further broken
down into their individual components both in Table
S-2 and in the discussion that follows.

Source Characteristics

Computer  codes  can  accommodate   the   spatial
distribution of the contaminant source in a number of
ways.  The most common are:

        Point source, such as a waste drum or tank,

        Line source, such as a trench, and

        Area  source,  such as ponds,  lagoons,  or
        landfills.

The determination of how the spatial distribution of
the source term should be modeled (i.e., point, line, or
area) is dependent on a number of factors, the most
important of which is the scale at which the site will be
investigated and modeled. If the region of interest is
very large, as compared to  the contaminant  source
area, even sizable lagoons  or  landfills could be
considered point sources.

The modeling objectives  are  also  important  in
determining the way in which the source term should
be  modeled.   For example, if simple scoping
calculations are being performed, treating the source as
a   point   will  yield   generally   conservative
approximations of contaminant concentrations because
of limited  dispersion.   However, if more realistic
estimates of concentrations and plume geometry are
required, it will be generally necessary to simulate the
source term characteristics more accurately, especially
if the receptor is close to a relatively large source.

In  addition to  the geometry of the source, code
selection is determined by whether the source is to be
modeled  as a  continuous or  time-varying release.
Computer codes  can simulate the introduction  of
contaminants to the ground water as an instantaneous
pulse or as  a  continuous  release over  time.   A
continuous release may either be constant or vary with
time.

The need to model the source as a constant or time-
varying release primarily depends on the half-life of
the radionuclide relative to the time period of interest
and whether average impacts or time-varying impacts
of a release are of interest. In general, the simplest
calculations, which assume a continuous release, are
sufficient when determining the average annual doses
to ground-water users at sites with relatively long-lived
radionuclides.

Aquifer and  Soil/Rock Characteristics

The most common site characteristics with regard to
aquifers that influence code selection  include  the
following:

    !    Confined aquifers

    !    Water-table  (unconfined) aquifers

    !    Convertible  aquifers

    !    Multiple aquifers/aquitards

    !    Heterogeneous aquifers

    !    Anisotropic  aquifers

    !    Fractures/Macropores

    !    Layered soils/rocks

Recognizing when and if these processes need to be
explicitly modeled is critical to the code selection
process.   There are no  simple  answers to  these
questions.  However, the following general guidance
may be helpful in making these determinations.

Confined versus Unconfined Aquifers

In most circumstances, the concern at a contaminated
site is contamination of unconfined aquifers since
sources  of   ground   water  generally  become
contaminated   by   leachate    migrating   from
contaminated surface soil through an unsaturated zone
of varying thicknesses to an  aquifer.   However,
confined aquifers could be of concern at sites where
contaminants were disposed in injection wells and
layered sites with "leaky aquitards."
Multiple Aquifers/Aquitards

Computer codes have been developed that have the
ability  to   simulate   either  single   or multiple
                                                  S-10

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hydrogeologic layers. Generally, a single-layer code is
used if the bulk of the contamination is confined to
that layer or if the difference in the flow and transport
parameters between the various layers is not significant
enough to warrant the incorporation of various layers.
It  generally does  not  make much sense to model
discrete  layers  if  estimated  parameter  values,
separating different layers, fall within probable error
ranges for the parameters of interest.  Furthermore,
unless the discrete hydrogeologic units are continuous
over the majority of the flow path, it is often possible
and preferable to model the system as one layer using
average flow and transport properties.

Layered Soil/Rocks in the Unsaturated Zone

Rarely would soils and rocks within the unsaturated
zone not exhibit some form  of natural layering. The
first consideration as to how this natural layering
should be treated in the modeling analysis is related to
whether  the various  soil layers have significantly
different flow  and transport properties.   If these
properties do not vary significantly from layer to layer,
there would be  little  need for the  code to have
multiple-layer capability.  On the other hand, if the
layers have distinctive properties that could affect flow
and transport, a decision needs to be made about how
best to achieve the modeling objectives;  i.e., should
each layer be discretely treated  or should all of the
layers be combined into a single layer.

Macropores/Fractures

Modeling flow through the unsaturated zone is based
on the  assumption  that  the  soil is a  continuous
unsaturated solid matrix that holds water within the
pores.  Actual soil, however, has a number of cracks,
root holes,  animal burrows,  etc., where the physical
properties differ enormously  from the surrounding soil
matrix.  Under appropriate conditions,  these flow
channels have the capacity to carry water at velocities
and concentrations that greatly exceed those in the
surrounding matrix.   Accordingly, it is critical to
determine whether ground-water flow and contaminant
transport at a site is dominated by macropores and
fractures because this factor could determine whether
a contaminant can reach the saturated zone  almost
immediately versus a  transit time on the order of
hundreds to thousands  of years.    This issue  is
especially  important   for   radionuclides   where
radioactive decay in transit  in the unsaturated zone
could virtually eliminate the concern over ground-
water contamination.

Anisotropic/Isotropic

In a porous medium made of spheres of  the same
diameter packed uniformly, the geometry of the voids
is the  same in  all directions.  Thus, the intrinsic
permeability of the unit is the  same in all directions,
and the unit is  said to be isotropic. On the other hand,
if the geometry of the voids is not uniform, and the
physical properties of the medium are dependent on
direction, the medium is said to be anisotropic.

In most sedimentary environments, clays and silts are
deposited as  horizontal layers.   This preferential
orientation  of  the  mineral  particles  allows  the
horizontal  velocity of the contaminants to  greatly
exceed those in the vertical direction. If anisotropy is
not taken into  account for the modeling analysis, the
contaminants will be predicted to be more dispersed in
the vertical direction than would probably be  occurring
in the real world.  The result could be an under-
prediction of the concentration of the contaminant in
the  centerline  and   an  over-prediction  of  the
contaminant concentration off-center in the vertical
direction.

Homogeneous/Heterogeneous

A homogeneous  unit  is  one that has  the same
properties  at  all  locations.   For  example,  for a
sandstone,  this  would  mean that the  grain-size
distribution, porosity, degree  of cementation,  and
thickness vary only within  small limits.  As a result,
the velocity and the volume of ground water would be
about the same  at all locations.  In heterogeneous
formations, hydraulic  properties change spatially.

For example, if it is expected that the aquifer thickness
will vary significantly (e.g., greater than ten percent),
a  computer code capable  of simulating  variable
thicknesses is  needed.  If a code does not properly
simulate  the  aquifer thicknesses, the contaminant
velocities will be too large   in  areas  where  the
simulated aquifer is  thinner than  the true  aquifer
thickness and too small in those regions that have too
great a simulated thickness.

The ability to simulate aquifer heterogeneities may also
be important during the remedial design phase of the
investigation.     If   engineered  barriers   of  low
                                                   S-ll

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permeability  are evaluated  as potential  remedial
options,  it would be necessary to determine  their
overall effectiveness.  In this scenario, it would not
only be important to select a computer code that has
the capability to simulate highly variable ground-water
velocities but also to ensure that the sharp changes in
ground-watervelocities do not cause instabilities in the
mathematical solutions.

Fate and Transport Processes

The  transport of radionuclides will be affected by
various  geochemical  and mechanical  processes.
Among the geochemical processes are adsorption on
mineral  surfaces and processes leading  to precipi-
tation.   These  processes  are  important primarily
because they reduce the velocity of the radionuclides
relative to the ground water (i.e., retardation), which
increases the transit time to  receptor locations and
results in additional radioactive decay in transit.

The following summarizes the primary processes that
affect the mobility and concentrations of radionuclides
being transported by ground water, including:

     !   Advection
     !   Dispersion
     !   Matrix Diffusion
     !   Retardation
     !   Radioactive Decay

Advection

The process by which solutes are transported by the
bulk movement of water is  known as advection. The
amount of solute that is being transported is a function
of its concentration in the ground water and the flow
rate of the ground water.

Computer codes that consider only advection are ideal
for designing remedial systems (e.g., pump and treat)
because the model  output  is in the form  of solute
pathlines (i.e., particle  tracks) which  delineate the
actual paths  that  a  contaminant  would follow.
Therefore, capture zones created by pumping wells are
based solely on hydraulic gradients and are not subject
to  typical  problems  that  occur  when  solving
contaminant   transport   equations  that   include
dispersion and diffusion.

Advective codes  are also excellent in the remedial
design  stage  for  determining  the  number  and
placement  of extraction or injection wells and in
evaluating the effect that low permeability barriers may
have on the flow system. They also tend to yield more
accurate  travel-time  determinations of  unretarded
contaminants  because the solution techniques  are
inherently  more stable, and  numerical oscillations,
which artificially advance the contaminant front, are
minimized. Another important advantage of advective
codes is that the output (i.e., particle tracks) are a very
effective  means of  ensuring  that  ground-water
gradients, both vertical and horizontal, are consistent
with the conceptual model.

Notwithstanding these advantages,  advective  codes
have some  drawbacks. The most significant of these
are their inability to address adsorption and  matrix
diffusion.  As discussed below,  these processes  can
determine the length  of time that a pump and treat
system must operate before clean-up goals will be met.
Without  the   ability  to  evaluate  the effects that
adsorption and diffusion may have on solute transport,
it would be very difficult to estimate remediation times.

A second  potential  problem with  advection-based
codes  is  that  dispersion  will  tend  to   spread
contaminants over a much wider area than would be
predicted if only advective processes are considered,
thereby underestimating the extent of contamination.
However, because dilution due to dispersion is under-
accounted for, unrealistically high peak concentrations
are generally obtained, which may be appropriate if
conservative  estimates are desired.  An additional
disadvantage  is  that pure  advection-based problems
result in hyperbolic  instead of  parabolic equations
which cannot be solved numerically due to severe grid
and time-step constraints.

Hydrodynamic Dispersion

In addition to advective transport,  the transport of
contaminants in porous media is also influenced by
dispersion  and diffusion,  which tend to  spread the
solute out from the path that it would be expected to
follow if  transported only  by  advection.    This
spreading of the contamination over an ever-increasing
area,  called   hydrodynamic  dispersion,  has  two
components:   mechanical dispersion and diffusion.
Hydrodynamic dispersion causes dilution of the solute
and occurs because of spatial variations  in ground-
water flow velocities  and  mechanical mixing during
fluid  advection.   Molecular diffusion, the  other
component of hydrodynamic dispersion, is due to the
                                                   S-12

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thermal-kinetic energy  of solute particles and also
contributes to the dispersion process.  Diffusion in
solutions is the process whereby ionic or molecular
constituents  move   in  the  direction  of   their
concentration gradient.    Thus,  if  hydrodynamic
dispersion  is factored  into  the  solute  transport
processes, ground-water contamination will cover a
much larger region than in the case of pure advection,
with  a  corresponding  reduction  in the  maximum
concentrations of the contaminant.

Matrix Diffusion

The  diffusion of radionuclides from water moving
within fractures, or coarse-grained material, into the
rock matrix or finer grained clays can be an important
means of slowing the  transport of the dissolved
radionuclides, particularly for non-sorbing  or low-
sorbing soluble species.

Matrix diffusion is frequently insignificant and is often
neglected in many of the contaminant-transport codes.
However, a number of potential problems arise when
matrix diffusion is ignored and contaminant velocities
are based solely  on advective-dispersive  principles.
For   example,   ground-water   pump   and   treat
remediation  systems  work on  the premise that  a
capture zone is created by the pumping well and all of
the  contaminants  within the  capture   zone will
eventually flow to the well.  The rate at which the
contaminants flow to the well may, however, be very
dependent on the degree to which the contaminants
have diffused into the fine grained matrix (e.g., clays).
This is because the rate at which they will diffuse back
out of the  fine grained materials may be strongly
controlled by concentration gradients, rather than the
hydraulic gradient created by  the  pumping well.
Therefore, matrix diffusion can significantly retard the
movement of contaminants, and, if the computer code
does not explicitly account for this process, the overall
effectiveness of the remediation system (i.e., clean-up
times) could be  grossly underestimated.  Matrix
diffusion processes can  also lead to erroneous model
predictions in the determination of radionuclide travel
times, peak concentrations, and flushing volumes.

In general,  matrix diffusion can be a potentially
important process in silty/sandy soil which contains
layers of clay or fractured rock.  Through the process
of matrix diffusion, the clay and rock can serve as
reservoirs of contaminants that slowly leak back into
the ground water over a long period of time.
Retardation

In addition to the physical processes, the transport of
  irHnrmHiHpc ic affprtpH hv rhpmiral nrnrpccpc  The
111 auuiiiun iu me jjiiy si^ai jjiu^csscs, me iidiisjjv
radionuclides is affected by chemical processes.
most important include:
    !   Sorption ~ the sorption of chemical species
        on mineral surfaces, such as ion exchange,
        chemisorption, van der Waals attraction, etc.,
        or ion exchange within the crystal structure.

    !   Ion  exchange phenomena ~ that  type of
        sorption restricted to interactions between
        ionic contaminants and geologic materials
        with charged surfaces which can retard the
        migration of radionuclides.

A wide range of complex geochemical reactions can
affect the transport of radionuclides, many of which
are poorly understood and are  primarily research
topics. From a practical view, the important aspect is
the removal of solute from solution, irrespective of the
process. For this reason, most computer codes simply
lump all of the cumulative effects of the geochemical
processes   into  a  single  term (i.e.,  distribution
coefficient) which describes the  degree to which the
radionuclide is retarded relative to the ground water.
Thus,   the   distribution   coefficient  relates  the
radionuclide   concentration   in   solution  to
concentrations adsorbed to the  soil.  Because the
distribution coefficient is strongly affected  by site-
specific conditions, it is frequently obtained from batch
or column  studies in which aliquots of the solute, in
varying  concentrations,   are   well   mixed   with
representative solids from the site, and the amount of
solute  removed  from  the water to  the  solid is
determined.

From the perspective of model selection, virtually all
computer codes explicitly address retardation through
the use of retardation factors, which are derived from
the distribution coefficient.  The primary  concern is
that the retardation factors are appropriate for the site
and  conditions  under consideration.   Spacial and
temporal changes in pH and the presence of chelating
agents could invalidate the retardation factors selected
for use at a site.

Radioactive Decay

Radionuclides decay to either radioactively stable or
unstable decay  products.   For  some radionuclides,
                                                   S-13

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several decay products may be produced before the
parent species  decays to  a stable element.  These
radioactive decay products may present a potentially
greater   adverse   health   risk  than  the  parent.
Accounting for the chain-decay process is particularly
important  for predicting  the potential impacts  of
naturally occurring radionuclides, such as uranium and
thorium, and transuranics.  In considering this process
over the transport path of radionuclides, one transport
equation must be written for each original species and
each decay product to yield the concentration of each
radionuclide (original species and decay products) at
points of interest along the flow path in order to
estimate total radiological exposures. However, not all
computer codes that simulate radioactive decay allow
for ingrowth of the decay products,  which may not
cause a problem  if the half-lives of the parent and
daughters are very long (i.e., it takes a long time for
the daughter products to  grow in) or if the decay
products are of little interest.

Multiphase Fluid Conditions

The movement of contaminants that are immiscible in
water  (i.e., non-aqueous  phase  liquids  - NAPL)
through the unsaturated zone and below the water table
results in systems that have multiple phases (i.e., air,
water, NAPL).  This  coexistence of multiple phases
can be  an important facet in many  contaminant-
transport analyses. However, only the water and the
vapor phase are generally of concern when evaluating
the transport of radionuclides. A limited number of
radionuclides can form volatile species that are capable
of being transported in a moving vapor or gas. Among
these  are  tritium, carbon-14,  radon-220/222,  and
iodine-129. Accordingly, if these radionuclides are
present,  vapor phase transport  may need to be
explicitly considered.

S.5 THE CODE  SELECTION PROCESS

Given that an investigator understands the various
waste/contaminant and site characteristics that need to
be  modeled  in order to  meet  specific  modeling
objectives, there will oftenbe several suitable computer
codes that  could potentially be chosen from a large
number of published codes presented in the scientific
literature.  Ideally, each candidate code should be
evaluated in detail to identify the one most appropriate
for the  particular  site and  modeling objectives.
However, the resources to complete a detailed study are
seldom available, and usually only one to two codes are
selected  based  upon  a  cursory  review  of code
capabilities and the experience of the modeler.

Regardless of whether  a detailed or more cursory
review is performed, it is important for the reviewer/
investigator to be cognizant of the following factors
and how they will affect code selection:

    1.   Code Capabilities consistent with:
          User needs
          Modeling objectives
          Site characteristics
          Contaminant  characteristics
          Quality and quantity of data

    2.   Code Testing
          Documentation
          Verification
          Validation

    3.   History of Use Acceptance

The  first aspect of the  review concentrates on the
appropriateness  of the  particular code to  meet the
modeling needs of the project. The reviewer must also
determine whether the data requirements of the code
are consistent with the  quantity  and quality of data
available from  the  site.   Next,  the  review must
determine whether the code has been properly  tested
for its  intended  use. Finally,  the code should have
some history of use on similar projects, be  generally
accepted within the modeling community, and readily
available to the  public.

Evaluating a code in each of the three categories can
be a significant undertaking, especially with respect to
code testing. Theoretically, the reviewer should obtain
a copy of the computer code,  learn to use the code,
select  a  set  of verification problems with known
answers, and compare the results of the model to the
benchmark problems. This task is complicated, largely
because no standard set of benchmark problems exists
and the mathematical formulation for each process
described within the code has to be verified through
the benchmarking  process.   It is recommended,
primarily  for this reason, that  the codes  selected
already be  widely  tested and  accepted.    Model
validation,   which  involves   checking the  model
predictions against  independent  field investigations
designed specifically to test the accuracy of the model,
would  almost never be practical during the code
evaluation and selection process.
                                                   S-14

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The model evaluation process involves the following
steps:

1.  Contact the author of the code and obtain the
    following:

    - Documentation and other model-related
    publications
    - List of users
    - Information related to code testing

2.  Read all  publications  related  to  the model,
    including  documentation, technical  papers, and
    testing reports.

3.  Contact code users to find out their opinions.

4.  Complete the written evaluation using the criteria
    shown in Table S-3.

Much  of the  information needed for  a  thorough
evaluation  can  be  obtained  from the author  or
distributor of the code. In fact, inability to obtain the
necessary publications can be an indication that the
code is either not well documented or that the code is
proprietary.  In either case, inaccessibility  of the
documentation and related publications should be
grounds for evaluating the code as unacceptable.

Most of the items in Table S-3 should be described in
the code documentation, although excessive  use of
modeling jargon may make some items difficult to
find.   For  this reason, some  assistance  from an
experienced modeler may be required to complete the
evaluation.  Conversations with users can also help
decipher cryptic aspects of the documentation.

The evaluation process must rely on user opinions and
published information to take the place  of hands-on
experience  and testing.  User opinions are especially
valuable in determining whether the code functions as
documented or has significant errors (bugs). In some
instances, users have performed extensive testing and
benchmarking or are familiar with published  papers
documenting the use of the code.   In essence, the
evaluation process substitutes second-hand experience
for first-hand knowledge (user opinions) to shorten the
time it takes to perform the review.
                                                   S-15

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                   Table S-3. Model Selection Criteria
                                  CRITERIA
Section 5.2.1    Administrative Data
                    Author(s)
                    Development Objective (research, general use, education)
                    Organization(s) Distributing the Code
                    Organization(s) Supporting the Code
                    Date of First Release
                    Current Version Number
                    References (e.g., documentation)
                    Hardware Requirements
                    Accessibility of Source Code
                    Cost
                    Installed User Base
	Computer language (e.g., FORTRAN)	
Section 5.2.2
Remedial Process
    Scoping
    Characterization
    Remediation
Section 5.2.3    Site-Related Criteria
                    Boundary/Source Characteristics
                            Source Characteristics
                                Multiple sources
                                Geometry
                                    line
                                    point
                                    area
                            Release type
                                constant
                                variable
                    Aquifer System Characteristics
                        confined aquifers
                        unconfined aquifers (water-table)
                        aquitards
                        multiple aquifers
                        convertible
                    Soil/Rock Characteristics
                        heterogeneity in properties
                        anisotropy in properties
                        fractured
                        macropores
                        layered soils
                    Transport and Fate Processes
                        dispersion
                        advection
                        diffusion
                        density dependent
                        partitioning between phases
                            solid-gas
	solid-liquid	
                                      S-16

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                          Table S-3. (Continued)
                                 CRITERIA
                           equilibrium isotherm:
                               linear (simple retardation)
                               Langmuir
                               Freundlich
                               nonequilibrium isotherm
                           radioactive decay and chain decay
                           speciation
                    Multiphase Fluid Conditions
                       two-phase water/NAPL
                       two-phase water/air
                       three-phase water/NAPL/air
                    Flow Conditions
                       fully saturated
                       variably saturated
                    Temporal Discretization (steady-state or transient)
Section 5.2.4    Code-Related Criteria
                    Source Code Availability
                    History of Use
                    Code Usability
                    Quality Assurance
                       code documentation
                       code testing
                    Hardware Requirements
                    Solution Methodology
                    Code Output
  	Code Dimensionality
                                     S-17

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                                            SECTION 1
                                        INTRODUCTION
1.1 BACKGROUND-PURPOSE AND SCOPE OF
    THE JOINT EPA/DOE/NRC PROGRAM

The   overall joint  EPA/DOE/NRC  program  is
concerned with the  selection and use of mathematical
models that simulate the environmental behavior and
impacts of radionuclides via all potential pathways of
exposure,  including the  air, surface water,  ground
water, and terrestrial pathways. Figure 1-1 presents an
overview of the various exposure pathways.

Though the joint  program is concerned with  all
pathways, it has been determined that, due to the
magnitude of the undertaking, it would be appropriate
to divide the program into smaller, more manageable
phases,  corresponding  to  each  of  the  principal
pathways of exposure. It was also determined that in
the first phase of the project greatest attention would
be given to the ground-water pathways.
Ground-water   pathways   were   selected  for
consideration first for several reasons.  At  a large
number of sites currently regulated by the EPA and the
NRC or owned by the DOE, the principal concern is
the existence of, or potential for, contamination of the
aquifers underlying  the various  sites.  In addition,
relative to  the air,   surface  water,  and terrestrial
pathways,  ground-water  contamination  is  more
difficult to sample and monitor, thereby necessitating
greater dependence on models to predict the locations
and levels of contamination in the environment.

The types of models  used to simulate the behavior of
radionuclides in ground water must be more complex
than surface water and atmospheric pathway transport
models in order to address the more complex settings
and the highly diverse types of settings associated with
different sites.  As a result, the methods used to
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                                                  1-1

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model ground water have not been standardized to the
same extent as has surface water and air dispersion
modeling, and, therefore, there is considerably less
regulatory guidance regarding appropriate methods for
performing ground-water modeling.

In addition to pathways of exposure, the scope of Phase
1 of the joint program also considered the range of
categories of sites that should be considered. The full
range  of sites in  the  United States that contain
radioactive materials can be divided into the following
categories:

   !  Federal facilities under the authority of 18 federal
     agencies, predominantly consisting of DOE and
     Department of Defense (DOD) sites and facilities,
     and sites listed on the National Priorities List
     (NPL),

   !  NRC  and NRC  Agreement  State  licensed
     facilities,

   !  State licensed facilities,

   !  Facilities and  sites  under the authority of the
     states but not governed by specific regulations.
     These include sites containing elevated levels of
     naturally occurring radionuclides (NORM).

All of these sites  are  of interest  to the  program.
However, a number of categories of facilities and sites
were excluded from consideration in the joint program
because they are being licensed specifically to receive
radioactive material for storage  and disposal; i.e.,
licensed low-level and high-level waste storage and
disposal sites. These sites are being managed within
a highly  structured regulatory  context to receive
radioactive materials,  and, though models are used to
support the siting and design of such facilities, they are
not remedial sites.

It  was  also  necessary  to limit  the range  of the
categories of sites of interest to the program in order to
keep the number of categories of sites to a manageable
size.  It was determined that this phase of the project
will be limited to (1) sites currently listed on the NPL
that  contain radioactive materials  and  (2)  sites
currently or formerly licensed by the NRC that are part
of the Site Decommissioning Management Program
(SDMP).  The  SDMP has been established  by the
NRC to decommission 46 facilities

that  require  special  attention by  the  NRC staff.
Ground-water modeling needed to support remedial
decision making at NPL sites containing radioactive
materials is in many ways similar to the ground-water
modeling needs of the SDMP.

These   categories  of  sites   were  selected  for
consideration because decisions are currently being
made   regarding  their   decontamination  and
remediation, which, in many cases, require the use of
models to support decision making and  demonstrate
compliance  with  remediation  goals.    Though the
project is designed to  address the modeling needs of
these categories of sites, the information gathered on
this project should have applicability to the full range
of categories of sites concerned with the disposition of
radioactive contamination.

In  conclusion, in order  to meet its  mission  of
promoting  the appropriate and  consistent  use  of
mathematical  models  in  the  remediation  and
restorationprocess at sites containing, or contaminated
with, radioactive materials, this first phase of the joint
program is designed to achieve the following four
objectives:

  1)   Describe   the  roles  of  modeling  and  the
       modeling needs at each phase in  the remedial
       process (MAU93);

  2)   Identify models in actual use at NPL sites and
       facilities licensed under RCRA, at DOE sites,
       and at NRC sites undergoing decontamination
       and decommissioning (D&D) (PAR92);

  3)   Produce detailed critical reviews of selected
       models in widespread use; and

  4)   Produce draft guidance for hy drogeologists and
       geoscientists tasked with the responsibility of
       selecting and reviewing ground-water flow and
       transport  models used  in the  remediation,
       decommissioning, and restoration process.

This report fulfills the fourth objective of Phase 1 of
the joint program.  Specifically, this report describes a
process for reviewing and selecting ground-water flow
and transport models that will aid remedial decision
making during each phase of the remedial process,
from the initial  scoping  phase, to  the detailed
characterization  of the  site, to the  selection  and
implementation of remedial alternatives.
                                                    1-2

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1.2  PURPOSE AND SCOPE OF THIS REPORT

Remedial contractors, with the concurrence of the site
managers, generally select and apply ground-water
flow  and  transport  models.    However,  unless
specifically trained in ground-water flow and transport
modeling, it is difficult  for  the site manager  to
participate actively in these decisions.  Ground-water
flow  and   transport  modeling  requires   highly
specialized training and experience, and,  as a result,
the site manager must usually depend heavily on the
expertise and judgement of staff hydrogeologists  as
well as  outside contractors and  consultants.   This
report provides background information that should
help hydrogeologists and geoscientists assist the site
manager in making more informed decisions regarding
the  selection  and use  of ground-water  flow and
transport models and computer codes throughout the
remedial process.

Previous reports in this series (MOS92, PAR92) have
determined that the types of models and the processes
that require modeling during  the remedial  process
depend on a combination of the following five factors:

   1.  reasons for modeling,
   2.  contaminant waste characteristics,
   3.  site environmental characteristics,
   4.  site land use and demography, and
   5.  phase of the remedial process.

The principal reasons for modeling  that, in part,
influence model selection include: (1) development
and refinement of the site conceptual model from
which hypotheses may be tested, (2) the performance
of risk assessments and the evaluation of compliance
with applicable health and safety regulations, (3) the
design of environmental  measurements  programs,
primarily  to  determine the optimal location for
boreholes, and (4) the identification, selection, and
design of remedial alternatives. Each of these reasons
for modeling influences modeling needs  and model
selection differently.

A review of the physical, chemical, and radiological
properties of the waste at a number of remedial sites
reveals that the waste characteristics can be diverse.
At sites  currently  undergoing  or  scheduled for
remediation, over 30 different types of radionuclides
have been identified, each  with its own radiological
and chemical  properties.   The  waste  is found in a
variety  of chemical  forms and physical  settings,
including contaminated soil, in ponds, in storage piles
and landfills,  buried in trenches, and in tanks and
drums.  Each of these physical and chemical settings
influences the areal distribution of the contaminants
and rate at which they may leach into the underlying
aquifer, which, in turn, influences model selection.

In a similar manner, the environmental characteristics
of remedial sites are highly diverse (PAR92).  The sites
containing radioactive materials that are currently
undergoing remediation include both humid and dry
sites, sites with and without an extensive unsaturated
zone,   and   sites   with  simple   and   complex
hydrogeological  characteristics.    These   different
environmental settings determine the processes that
need to be modeled, which, in turn, influence the
selection of models and computer codes.

The land use and  demographic patterns at a site,
especially the location and extent of ground-water use,
affect the types and complexity of the models required
to assess the  potential impacts of the site on public
health.   At many  of the  sites  contaminated with
radioactive materials, the principal concern is the use
of the  ground water by  current or future  residents
located close to, and downgradient from, the source of
contamination. At other sites, the concern is the use of
private and municipal wells located at some distance
and in a variety of directions from the source. Each of
these usage patterns influences the selection of ground-
water flow and transport models and computer codes.

Superimposed on these waste and site-related issues
are the different modeling needs associated with the
various phases of the remedial process.  The phase of
the remedial process from  scoping and planning, to
site characterization, to  remediation, creates widely
different opportunities for modeling, which, together
with the other factors,  influences  model and code
selection.

This report describes the methods for selecting ground-
water flow and transport models and computer codes
that meet the  modeling needs at sites contaminated
with radioactive materials.  The selection process is
described in terms  of the various site characteristics
and processes requiring modeling and the availability,
reliability, and costs of the computer codes that meet
the modeling needs.

Though this report is limited to a  discussion of the
model  selection process, it is  recognized  that the
proper  application of the  selected models is as
important, if not more important, than model selection.
A model, no  matter how well suited to a particular
application,   could  give  erroneous  and highly
                                                   1-3

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misleading  results  if used  improperly  or  with
incomplete or erroneous input data. Conversely, even
a model with very limited capabilities, or a model used
at a site which has not been well characterized, can
give very useful results if used intelligently and with a
full appreciation of the limitations of the model and
the input data. It is not possible within the scope of
this project  to address model applications,  quality
control, and the presentation and interpretation  of
modeling results. Future reports prepared under this
program will address these important topics.

1.3  PRINCIPAL SOURCES OF INFORMATION

In accomplishing its objectives, this report makes use
of the information contained in the previous  reports
prepared on this program, including:

  ! "Environmental Pathway Models - Ground Water
    Modeling in  Support of Remedial Decision
    Making at Sites Contaminated with Radioactive
    Material," EPA 402-R-93-009, March 1993.

  ! "Environmental Characteristics of EPA, NRC,
    and DOE Sites Contaminated with Radioactive
    Substances," EPA 402-R-93-001, March  1993.

  ! "Computer Models Used to  Support Cleanup
    Decision Making at Hazardous and Radioactive
    Waste Sites," EPA 402-R-93-005, March 1993.

In addition, extensive use was made of:

  ! "Superfund  Exposure  Assessment  Manual,"
    EPA/540/1-88/001, April 1988.

  ! "Leachate Plume  Management,"  EPA/540/2-
    85/004, November 1985.

  ! IMES,  "Integrated Model Evaluation System,"
    Prototype,  Version  1,  September   1991.
    Developed by  Versar, Inc.  for the Exposure
    Assessment  Group,  Office   of Health  and
    Environmental Assessment, Office of Research
    and Development,  Environmental  Protection
    Agency.

Finally, this  report relies heavily on  the experience
gained by the project team during the review of three
existing codes: RESRAD, VAM2D, and MT3D. As
part of this project, these three computer codes were
reviewed as if they were being considered for use on a
remedial project. The review of these codes, including
the process  used to  review these  codes, has been
documented in a separate report (EPA 402-R-93-005)
in this series.  The procedures used to perform these
reviews contributed to the generic guidance presented
in this report.

1.4 KEY TERMS

A glossary of terms used in this report is presented in
Appendix A. In addition, an index directs the reader
to the pages in  the report where key terms are defined
and  discussed.   Described below are  three key
terms/concepts that are fundamental to understanding
the report.

Conceptual Model. The conceptual model of a site is
a flow diagram, sketch, and/or description of a site and
its setting.  The  conceptual model describes  the
subsurface  physical  system including the nature,
properties, and variability of the aquifer system (e.g.,
aquifers, confining units), and also depicts the types of
contaminants/wastes at a site, where they are located,
and how they are being transported offsite by runoff,
percolation into the ground and transport offsite in
ground water, or suspension or volatization into the air
and  transport   by  the  prevailing  meteorological
conditions.  The conceptual model also attempts to
help visualize the direction and path followed by the
contaminants, the actual or potential locations of the
receptors,  and  the  ways in which receptors may be
exposed,  such  as  direct contact with the source,
ingestion of contaminated food or water, or inhalation
of airborne contaminants.  As information regarding a
site accumulates, the conceptual model is continually
revised and refined.

Mathematical  Model.     A  mathematical  model
translates  the  conceptual model into  a series  of
equations which, at a minimum, describe the geometry
and dimensionality of the system, initial and boundary
conditions, time dependence,  and the  nature of the
relevant  physical  and chemical  processes.   The
mathematical  model  essentially  transforms  the
conceptual model to the level of mathematical accuracy
needed to support remedial decision making.

Computer Code. A computer code is simply a tool that
is used to solve the  equations which constitute the
mathematical model of the site and display the results
in a manner convenient to support remedial decision
making.
                                                  1-4

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1.5  ORGANIZATION OF THE REPORT

This report is divided into five sections.  Following
this introduction, Section 2 presents an overview of the
types of ground-water modeling decisions facing the
site remediation manager.  The section is designed to
help the site manager determine the role of, and need
for, modeling in support of remedial decision making.

Section 3 addresses the construction of a conceptual
model  of a site and  how  it is used in the initial
planning and scoping phases of a site remediation,
especially as it pertains to  the selection and use of
ground-water flow and contaminant transport models.

Section 4 describes the various site characteristics and
ground-water   flow  and   contaminant  transport
processes that may need to be explicitly modeled.  The
purpose of this section is to help the site manager
recognize the conditions under which specific model
features  and  capabilities  are  needed  to  support
remedial decision making during each phase in the site
remediation process.

Section 5 summarizes the computer code attributes that
should be considered for screening and selecting the
potential computer codes that are best  suited  to meet
site-specific modeling needs.
                                                   1-5

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                                            SECTION 2

                        MODELING DECISIONS FACING THE SITE
                                  REMEDIATION MANAGER
A review of current regulations and guidelines pertaining to the remediation of sites on the National Priorities List and
in the Nuclear Regulatory Commission's Sites Decommissioning Management Program (SDMP) reveals that fate and
effects modeling is not explicitly required.  However, in order to make informed and defensible remedial decisions,
ground-water flow and transport modeling can be useful. This section presents a methodology for determining when
ground water may be a significant pathway of exposure and discusses the roles ground-water modeling may play in
support of remedial decision making. The section concludes with a discussion of the various resources available to the
remediation manager to help in identifying and fulfilling modeling needs.
2.1 IS  GROUND  WATER A POTENTIALLY
    IMPORTANT EXPOSURE PATHWAY?

The  ground-water pathway  may  be considered a
potentially significant exposure pathway if:  (1) the
radionuclide  concentrations  in the ground water
exceed the levels acceptable to the cognizant regulatory
authorities; or (2) the contamination at the site could
eventually cause the radionuclide  concentrations in
ground water to exceed the applicable criteria. On this
basis, if the measured concentrations of radionuclides
in ground water downgradient from the site, or in
leachate at the site, exceed the applicable criteria, and
the ground water in the vicinity of the site is being
used,  or has the  potential to be used as a source of
drinking water, it is likely that ground-water modeling
will be useful, if not necessary, in support of remedial
decision making at the site.

Until  additional regulatory guidance is available, the
drinking water standards set forth in 40  CFR  141
should guide remedial decision making.  Section 1412
of the Safe Drinking Water Act (SDWA), as amended
in  1986,  requires   EPA  to  publish  Maximum
Contaminant Level Goals (MCLGs) and promulgate
National Primary Drinking Water Regulations for
contaminants in drinking water which may cause any
adverse effects on the health of persons and which are
known or anticipated to occur in public water systems.
On July 9, 1976, the EPA published "Interim Primary
Drinking  Water  Regulations,  Promulgation  of
Regulations on Radionuclides" (41 FR 28402).

The interim rule establishes maximum contaminant
levels (MCL) for radionuclides in community water.
The MCLs limit the concentration of radionuclides at
the tap to:

   !    5 pCi/L for Ra-226 plus Ra-228.
   !    15 pCi/L for gro ss alpha, including Ra-226 but
       excluding radon and uranium.

   !    that concentration of manmade beta/gamma
       emitting  radionuclides  that  could  cause
       4 mrem/yr to the whole body or any organ.

The  regulation applies to  community public water
systems  regularly   serving  at  least 25  persons
year-round or having at least 15 connections used
year-round.

In response to a need to finalize the rule,  expand the
regulations to include uranium and radon, and revise
and refine the rule, the EPA published an Advanced
Notice of Proposed Rulemaking (ANPR) on September
30,1986(51FR 34836), and onJuly 18,1991theEPA
issued an NPR entitled "National Primary Drinking
Water Regulations; Radionuclides" (56 FR 33050). 40
CFR 191 is being finalized.

As in the interim rule, the proposed rule applies to all
community, and all non-transient, non-community
public water systems  regularly  serving at least 25
persons year-round or having at least 15 connections
used year-round. The proposed standards establish the
following requirements:

   The Maximum Contaminant Level  Goal (MCLG)
   for all radionuclides is zero since radionuclides are
   known carcinogens. MCLGs are non-enforceable
   health goals that are set at levels at which no known
   or  anticipated adverse effects on  the  health of
   persons occur and which allow an adequate margin
   of safety.
  The MCLs are as follows:
                                                  2-1

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  Radionuclide
MCL
  Ra-226                  20 pCi/L
  Ra-228                  20 pCi/L
  Rn-222                  300 pCi/L
  Uranium                 20 ug/L (30 pCi/L)
  Beta and photon emitters
     (excluding Ra-228)     4 mrem/yr EDE
  Adjusted gross alpha
     emitters (excluding
     Ra-226, U, and Rn 222)   15 pCi/L

MCLs are enforceable standards set as close to the
MCLGs  as is feasible, including economic factors.
The   proposed   rule   also   establishes   specific
requirements  regarding  the  use   of  control  and
treatment technologies and monitoring and reporting
requirements.

The drinking water standards are fundamental health-
based  standards that  apply  to public sources  of
drinking water.  In  addition, the drinking water
standards have also had extensive use as applicable or
relevant and appropriate regulations (ARARs) forNPL
sites. As an ARAR, if the observed concentrations of
radionuclides in drinking water supplies coveredby the
rule  exceed  the MCLs, the rule applies directly and
remedial actions are required.  If the potential exists
for ground-water contamination to exceed the MCLs,
the rule is considered relevant and appropriate.

For NPL  sites, the  Hazard Ranking System (HRS)
scoring package provides information that will help in
determining if ground-water modeling is needed at a
site.  Specifically, Section 7.1.1 of the HRS  requires
the   sampling and  analysis  of  ground  water  to
determine if ground-water contamination is  present.
If radionuclide concentrations in  ground water in
excess of background are found and exceed the Level
I benchmarks delineated in Sections 2.5.2 and 7.3.2 of
the HRS (these benchmarks are keyed to the MCLs),
ground-water contamination is a concern at  the site,
and ground-water modeling will likely  be needed to
support the  baseline risk assessment and remedial
decision making.

At some  sites, information may  not  be available
regarding the levels of radionuclide contamination in
ground water or leachate. Alternatively, radionuclide
measurements  may  have  been  made,  but  yield
inconclusive  results.   Under these conditions, an
estimate needs  to  be  made of  the  radionuclide
concentrations in the soil or the waste at the  site,
which can then be used to determine if the potential
exists for exceeding the applicable criteria.

For NPL sites, the information needed to make this
determination is likely  to be  available  in the HRS
scoring package addressing Hazardous Waste Quantity
and Likelihood of Release.  The preferred method for
scoring Hazardous Waste Quantity (Section 7.2.5.1 of
the HRS) requires information on the concentration of
individual radionuclides at the site and the volume and
area of the contamination.

Given the radionuclide concentrations in soil or waste,
the radionuclide  concentration in leachate  can be
estimated  using partition factors.  A partition factor
establishes the equilibrium relationship between the
average radionuclide concentration in soil or waste and
that in leachate.  If the product of the radionuclide
concentrations with the  appropriate partition factors
results in radionuclide  concentrations  in leachate
significantly in excess of the applicable criteria, it may
be concluded that the radionuclide concentrations in
ground water in the vicinity of the site could exceed
the criteria, thereby requiring ground-water modeling
to assess  the potential impacts  on nearby  user
locations.

Once  the leachate  comes  into  contact with  the
underlying soil, a  new equilibrium begins to be
established between the leachate and the soil.  The
equilibrium ratio of the radionuclide concentration in
the soil to that in the water in intimate contact with the
soil is referred to as the  distribution coefficient (Kd).
Once  site-specific Kds are determined or appropriate
generic   Kds  are  identified,  the  radionuclide
concentration  in the soil divided by the  Kd for each
radionuclide   yields  a crude  estimate  of  the
concentration of the radionuclide in the soil pore water
percolating through the soil.

Though partition factors are  highly site specific,
generic values have been used in the past for screening
calculations which are designed to provide reasonable
upper bound radionuclide concentrations in leachate
and ground water.   Examples of generic partition
factors are provided in NRC86. Tabulations of Kd
values that  have  had  widespread application  are
provided in BAE83  and  SHE90.

If either the  measured or  derived  values  for  the
radionuclide concentrations  in ground water exceed
the applicable criteria, resources need to be put into
place  to perform ground-water modeling.
                                                   2-2

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2.2  REASONS FOR MODELING

Once it is determined that the ground-water exposure
pathway  is potentially important, ground-water flow
and transport modeling can have a wide range of uses
in support  of remedial decision making.   Table 2-1
presents  the  principal reasons for modeling on a
remedial project.  These uses can surface during any
phase of the remedial process. However, some of these
reasons are more likely to occur during specific phases
of a remedial project.

In Table  2-1, scoping and planning occur early in the
project,  wherein  regional, sub-regional,  and site-
specific data are reviewed and analyzed in order to
define  the  additional data and analyses needed  to
support  remedial  decision  making.   In the site
characterization phase, the plans developed during the
scoping phase are implemented. These data are used
to characterize more fully the nature and extent of the
contamination at the site, to define the environmental
and  demographic characteristics of the site, and  to
support assessments of the actual or potential impacts
of the  site.  The results of the site characterization
phase  are  analyzed  to  determine  compliance with
applicable regulations and to begin to define strategies
for the  remediation of the site. In the site remediation
phase,  alternative remedies are identified, evaluated,
selected, and implemented.

During scoping and planning, modeling can be used to
identify the potentially significant radionuclides and
pathways of exposure, which, in turn, can be used to
support the design of comprehensive and cost-effective
waste characterization, environmental measurements,
and  site characterization programs.   During site
characterization, modeling is used primarily in support
of dose and risk assessment of the site and to evaluate
the adequacy of the  site  characterization program.
During the remediation phase, modeling  is used
primarily to support the selection and implementation
of alternative remedies and, along with environmental
measurements programs, is used  to determine the
degree to which the remedy has achieved the remedial
goals.

Table 2-1 attempts to identify those opportunities for
modeling that are more likely to surface during the
different phases of the remedial process.  In  general,
the remedial phase often dictates the types of remedial
decisions that need to be made and the amount of site-
specific information and time available to make these
decisions.   These,  in turn, determine the  role  of
modeling. For example, during scoping, it may not be
feasible to gain access to  sampling locations, and the
only way to predict the potential impacts of a source of
contaminants   is  by   modeling.    During   site
characterization,  sampling locations  are generally
accessible; however, the contaminant may have notyet
reached a receptor location. Accordingly, modeling is
used  to  predict  future  impacts.   During  remedy
selection,  modeling   is   used   to  simulate   the
performance of a remedy  in order to  evaluate its cost-
effectiveness and  refine its design.

2.3 PLANNING FOR MODELING

2.3.1   Identifying Modeling Needs

Given the  phase in the  remedial process and  the
reasons for modeling,  the types of models  and  the
input  data required to run the models are determined
by  the  characteristics  of  the waste,  the   site
hydrogeological setting and characteristics,  and  the
current and projected ground-water use in the vicinity
of the site.  Accordingly, the role  of and need  for
modeling, and the types of models and associated input
data, are determined by a combination of five factors:

   ! phase of the remedial process,
   ! reasons for modeling,
   ! waste characteristics,
   ! hydrogeological characteristics, and
   ! local land use and demography.

In order to make informed decisions regarding  the
selection and application of ground-water flow  and
transport models and the  interpretation of the results,
the remediation manager will  require site-specific
information on each of these five factors. The first two
factors are related and  are largely determined by  the
regulatory structure within which remedial decisions
are being made. The last three factors are of a more
technical nature and usually require highly specialized
expertise to  relate  the waste,  hydrogeologic,  and
demographic characteristics of a site to the models
suited to these characteristics and  the  reasons  for
modeling.
                                                   2-3

-------
                        Table 2-1.  Matrix of Reasons for Modeling
Opportunities for Modeling
1.
2.
3.
4.
5.
6.
7.
8.
When it is not feasible to perform field
measurements, i.e.,
! Cannot get access to sampling locations
! Budget is limited
! Time is limited
When there is concern that downgradient locations
may become contaminated at some time in the future.
When field data alone are not sufficient to
characterize fully the nature and extent of the
contamination; i.e.,
! when field sampling is limited in space and time
and needs to be supplemented with models
! when field sampling results are ambiguous or
suspect
When there is concern that conditions at a site may
change, thereby changing the fate and transport of
the contaminants; i.e.,
! seasonal changes in environmental conditions
! severe weather (floods, tornadoes)
! accidents (fire)
When there is concern that institutional control at the
site may be lost at some time in the future resulting
in unusual exposure scenarios or a change in the fate
and transport of the contaminants; i.e.,
! trespassers
! inadvertent intruder
! (construction/agriculture)
! drilling, mineral exploration, mining
! human intervention (drilling, excavations,
mining)
When remedial actions are planned and there is a
need to predict the effectiveness of alternative
remedies.
When there is a need to predict the time when the
concentration of specific contaminants at specific
locations will decline to acceptable levels (e.g.,
natural flushing).
When there is concern that at some time in the past
individuals were exposed to elevated levels of
contamination and it is desirable to reconstruct the
doses.
Scoping1
M
M
M
F
F
F
F
F
Site
Characterization1
F
M
M
M
M
F
M
M
Remediation1
F
M
M
M
M
M
M
F
1.  M Denotes an important role.
   F Denotes a less important role.
2-4

-------
                                  Table 2-1. (Continued)

Opportunities for Modeling
9.

10.



11.


12.



13.

14.

15.

16.

17.


18.



19.



20.


When there is concern that contaminants may be
present but below the lower limits of detection.
When field measurements reveal the presence of
some contaminants and it is desirable to determine if
and when other contaminants associated with the
source may arrive, and at what levels.
When field measurements reveal the presence of
contaminants and it is desirable to identify the source
or sources of the contamination.
When there is a need to determine the timing of the
remedy; i.e., if the remedy is delayed, is there a
potential for environmental or public health impacts
in the future?
When there is a need to determine remedial action
priorities.
When demonstrating compliance with regulatory
requirements.
When estimating the benefit in a cost-benefit analysis
of alternative remedies.
When performing a quantitative dose or risk
assessment.
When designing the site characterization program
and identifying exposure pathways of potential
significance.
When there is a need to compute or predict the
concentration distribution in space and time of
daughter products from the original source of
radionuclides.
When there is a need to quantify the degree of
uncertainty in the anticipated behavior of the
radionuclides in the environment and the associated
doses and risks.
When communicating with the public about the
potential impacts of the site and the benefits of the
selected remedy.

Scoping1
F

F



M


F



F

M

F

F

M


M



M



M


Site
Characterization1
M

M



M


F



F

M

F

M

F


F



F



F



Remediation1
F

F



F


M



M

M

M

M

M


F



F



M


  Source: EPA93
1.  M Denotes an important role.
   F Denotes a less important role.
2-5

-------
Recognizing the need for modeling, and identifying
and applying the models that meet these needs, unfolds
as the project matures.  Modeling decisions are based
on site-specific information pertaining to each of the
above five factors and the combined judgement of
regulatory  and  technical  specialists.   Modeling
decisions cannot be made in a "cookbook" fashion.
Accordingly,  during the initial phases of a remedial
project  and throughout  the  remedial process,  the
remediation manager must continually assess the need
to employ models.   Table  2-1  can be useful  in
determining when these needs exist or may arise.

Once the  modeling  needs  are  recognized, it  is
appropriate to determine or define  the  form of the
results or output of the modeling exercise.  The
following presents the various types of output resulting
from a given modeling exercise for sites containing
radioactive material.

 ! The time-averaged and time-varying radionuclide
  concentrations in air, surface water, ground water,
  soil, and food items. These are usually expressed in
  units  of pCi/L  of water or pCi/kg of soil  or food
  item.    The  time-averaged  values  are  used  to
  determine  the  annual radiation doses and risks
  and/or compliance with ARARs that are expressed
  as average, as opposed to peak values. The time-
  varying values are  useful  in determining  arrival
  times of contaminants at receptor locations, which
  can help in prioritizing  sites,  or the  impacts  of
  accidental releases, which are often one-time, short-
  term occurrences.

 ! The radiation field in the  vicinity  of radioactive
  material, expressed in units of uR/hr. Estimates of
  exposure rate, whether measured or predicted, are
  useful in protecting  members of  the public  or
  workers who may be present in, or need to enter, the
  radiation field.

 ! The transit time or time of arrival of a radionuclide
  at a receptor location. This measure is useful in
  determining at what point in the future a source of
  contamination has the potential to adversely affect
  receptors.

 ! The volume of water contained within or  moving
  through a hydrogeological setting.

 ! Potentiometric surfaces (i.e., heads)  are commonly
  output from ground-water flow models from which
  ground water/contaminant flow paths and/or capture
  zones can be determined.

!  Radiation doses to individual members of the public
  under quasi-steady state and changing conditions
  and following accidents.  The doses are evaluated
  for the site in its current condition (i.e., the  no
  action alternative) and during and following a broad
  range of feasible alternative remedies.  These are
  usually expressed in units of mrem/yr effective dose
  equivalent (EDE) for continuous exposures and
  mrem per event (EDE) for transients and postulated
  accidents.  Most radiation protection standards are
  expressed in units of the dose to individuals.

!  Radiation risks to individual members of the public
  under  expected   and transient conditions  and
  following accidents.  The risks are evaluated for the
  no action alternative and during and following a
  broad range of feasible remedies. These are usually
  expressed in units of individual lifetime risk of total
  and fatal cancers. In addition  to individual dose,
  individual risk is used to characterize the impacts on
  public  health  and  is required by  the National
  Contingency Plan (NCP).

!  Cumulative radiation doses to the population in the
  vicinity of the site under expected  and transient
  conditions and following accidents. The cumulative
  doses are evaluated for the no action alternative and
  during  and following a broad range of feasible
  remedies.  These are  usually expressed in units of
  person  rem/yr (EDE)  for continuous exposures and
  person  rem per event (EDE)  for transients and
  accidents.

!  Cumulative radiation risks to the population in the
  vicinity of the site under expected  and transient
  conditions and following accidents. The cumulative
  population risks  are  evaluated  for the no action
  alternative and during and following a broad range
  of feasible remedies.  These are usually expressed
  in units  of total  and  fatal cancers per year for
  continuous exposures or per event for transients and
  accidents in the exposed population.

!  Radiation doses and risks to remedial workers for a
  broad range of alternative remedies.  The units of
  dose and risk for  individual  and  cumulative
  exposures are the same as those for members of the
  public.

!  Uncertainties in the above impacts, expressed as a
  range  of values or a  cumulative  probability
                                                   2-6

-------
  distribution of dose and risk.

The specific regulatory requirements that apply to the
remedial program determine which  of these  "end
products" is needed. In general, these modeling results
are used  to assess impacts  or compliance  with
applicable regulations; however, information regarding
flux, transport times, and plume arrival times is also
used to support a broad range of remedial decisions.

These modeling endpoints must  be clearly  defined,
since the type of endpoint will help to determine the
type  of ground-water flow and transport model that
will support the endpoint of interest. For example, a
baseline risk assessment at a site contaminated with
radioactive material is used in determining the annual
radiation dose to an individual drinking water obtained
from a potentially contaminated well. The endpoint in
this case is the dose to an individual expressed in units
of mrem/yr.  In  order to estimate this dose, it  is
necessary to estimate the average concentration of
radionuclides in the well water over the course of a
year. The models, input parameters, and assumptions
needed to predict the annual  average radionuclide
concentration are different than those needed to predict
the time-varying concentration at a given location.
The latter usually requires much more input data and
models capable of simulating dynamic processes.

2.3.2   Sources of Assistance

Once the remediation manager has identified the role
modeling will play on the remedial project (see Table
2-1)  and the forms  of the  results of the modeling
exercise, resources must be put into place to meet these
needs.  These resources include  access to technical
expertise and a broad range of ground-water flow and
transport models.

In response  to the need for ground-water flow and
transport modeling in support of remedial  decision
making,  guidance  and  assistance  are  becoming
increasingly  available.      Appendix  B   briefly
summarizes  some of the resources  available to a
remediation manager, organized according to the
following categories:

   ! Branches and Divisions within Agencies
   ! Expert Systems
   ! Electronic Bulletin Boards
   ! Electronic Networks
2.3.2.1  Branches and Divisions Within Agencies

Environmental Protection Agency

Technical assistance available to EPA remediation
managers is described  in  "Technical Assistance
Directory," CERI-91-29, July 1991.

Nuclear Regulatory Commission

Technical assistance to NRC personnel with regulatory
oversight responsibility for the decontamination and
decommissioning of licensed facilities is  available
from  the  Office of Nuclear Material  Safety  and
Safeguards (NMSS).

Department of Energy

Technical guidance for DOE and DOE contractor
personnel with  responsibility  for  environmental
restoration and waste management at DOE facilities is
provided through the Office of Environmental, Safety,
and Health.  In addition, since many of the DOE sites
are on the NPL, EPA technical assistance can also be
accessed.

2.3.2.2  Electronic Media

Electronic communication media  are  becoming a
common means  by which individuals participate in
forums where expertise is freely shared.  Institutions
whose mandate includes the dissemination of expert
advice and information also use these media. These
forms  of communication  result  from the  direct
transmittal of computer media (e.g., tape, diskette, CD-
ROM, etc.)  or  utilize  remotely  accessed  computer
systems  consisting  of  dedicated hardware   and
associated software. In remote systems, the user can
access the system via modem or some other hard-wired
connection and retrieve from or transmit to the system
information as required.

Electronic media offer great potential to assist ground-
water model users and reviewers.  It is possible to
classify these media into three types, namely bulletin
boards (restricted access), networks (general access),
and expert systems.  Although the  first two systems
operate  similarly  and  share some approaches to
providing their  services, they differ in the way  that
they are used. A brief overview of these instruments
follows.  Specific examples of these  resources are
presented in Appendix B.
                                                  2-7

-------
Bulletin Boards

Bulletin boards exist at a specific location maintained
by an identifiable individual or institution.  Bulletin
boards usually contain facilities for posting electronic
mail and allow the user to participate in one or more
conferences - more-or-less structured discussions on
specific topics.  In addition,  most bulletin boards
contain archives of files consisting of various data
bases, executable programs, and notices.

Networks

A computer network consists of a number (in some
cases many thousands) of individual computers (nodes)
tied together by hardware and some network software
that regulates access to the system and the transfer of
information between nodes. Most network discussion
groups are moderated by  an individual or group of
individuals. Networks can be and are used to post
electronic mail in much the same way as one would
post mail on a bulletin board. However, they have the
additional capability of "broadcasting" information to
a much more general audience.  Networks are a good
way  to get answers to problems when the user is
unsure of who might possibly provide those answers.
An even more powerful aspect of some networks is the
ability to run software on  one of the  network nodes
in real-time from a
remote location with immediate feedback.   Most
bulletin boards don't allow that level of access.

Expert Systems

Expert systems are software packages which guide a
user through the solution of a problem by  asking a
series of questions and/or by providing a series of pre-
programmed answers to those questions. An example
of such a system that can be used in the selection of an
appropriate code for  air, surface, or ground-water
modeling is the Integrated Model Evaluation System
available from the Environmental Protection Agency.
Both bulletin boards and networks are effective  in
obtaining non-urgent help on focused issues and for
keeping up with fast-changing subjects - they are not
particularly useful  if  the user needs  information
quickly or  cannot phrase  a question succinctly and
clearly. Many bulletin boards and networks are free to
the user while others are based on some fee system.
Nearly all remotely accessed electronic media require
some form of registration before use, either by written
request and registration or by on-line registration
during the  user's  first session.  Expert systems will
usually offer the fastest and most in-depth answers to
specific problems. But expert systems can be quickly
outdated if the data  (knowledge) base on which they
depend changes.  The  "learning curve" for all three
types of electronic information exchange is fairly quick
- a user can request and/or obtain useful information in
a matter of minutes to hours.

-------
                                           SECTION 3

            CONSTRUCTING AND REFINING THE CONCEPTUAL MODEL
                                          OF THE SITE
For sites on the NPL, the development of a conceptual model of the site is identified as a specific step in the scoping
stage of the RI/RS process (see EPA88).  However, the need for conceptual modeling applies to any site undergoing
remediation. Figure 3-1, taken from EPA88, is an example of a conceptual model. It identifies the various pathways
that may contribute to the potential current and future impacts of the site on public health and the environment.
Accordingly, the construction of a conceptual model of a site is the first step in determining modeling needs and
identifying models that meet these needs.  This section presents a brief discussion of basic concepts pertinent to the
construction of a conceptual model of the site with respect to the ground-water pathway for sites contaminated with
radionuclides.
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3.1  BASIC QUESTIONS THAT WILL NEED TO
     BE ANSWERED

For  sites  where  ground-water  contamination  is
identified as a potentially important exposure pathway,
the planning effort should  attempt  to  answer the
following typical questions:

   !  Do the radionuclides have relatively long or short
     half-lives and do they have radioactive daughters?

   !  Do the contaminants enter the ground-water flow
     system at a point, or are they distributed along a
     line  or over an area (or volume)?

   !  Does the source  consist of an initial pulse of
     contaminant or is it constant over time?

   !  Is there a thick unsaturated zone?

   !  Is the lithography relatively homogeneous or does
     it contain multiple layers?

   !  How will  the hydrogeology  affect flow  and
     transport?

   !  At what rate will the radionuclides be transported
     relative to ground-water flow?

   !  Are  there nearby wells  or other hydraulic
     boundaries that could  influence ground-water
     flow?

   !  What is the nature of the system boundaries?

   !  Where are the current or future receptors located?
     Can they influence ground-water flow?

The answers to these questions will help to identify the
types of processes that may need to be modeled at the
site, which, in turn, will help in screening the types of
models and computer codes appropriate for the site.  A
discussion of the various flow and transport processes
and  the  site  characteristics that influence these
processes is provided in EPA88.

During the  scoping phase,  it will  not be possible, nor
necessary, to answer these questions  with certainty.
However,  as   site   characterization   proceeds,
information will become available that will help to
develop more complete answers to these questions. In
fact, a well-designed site characterization program will
obtain data that will help answer these questions.

3.2  COMPONENTS OF  THE CONCEPTUAL
     MODEL  FOR  THE  GROUND-WATER
     PATHWAYS

The components that make up the initial conceptual
model of the site include:

 1.   the contaminant/waste characteristics,

 2.   the site characteristics,  and

 3.   land use and demography.

As the remedial process progresses from initial scoping
and   planning  to   detailed  characterization  to
remediation, the site characterization becomes more
precise and complete. The following sections discuss
each of these components of a conceptual model and
how they can influence model selection.

3.2.1 Contaminant/Waste Characteristics

To the extent feasible, the site conceptual model should
address the following characteristics of the waste:

    ! Types of radionuclides

    ! Waste form and containment

    ! Source geometry (e.g., volume, area, depth,
     homogeneity)

    ! Physical and chemical properties of the
        radionuclides

    ! Geochemical setting

Within the context of ground-water modeling, these
characteristics  are pertinent  to modeling the source
term,  i.e., the  rate  at  which  radionuclides  are
mobilized from the  waste  and enter the unsaturated
and saturated zones.

Types of Radionuclides

One  of  the  most important  characteristics  in
developing a conceptual model of the site is identifying
the  type   and   approximate  quantities  of  the
radionuclides present. This will not only determine
the potential offsite impacts of the site, it will also help
                                                   3-2

-------
to identify the potential magnitude of the risks to
workers, the  mobility of the radionuclides, and the
time period over which the radionuclides may be
hazardous.    The types of radionuclides will also
determine whether radioactive decay and the ingrowth
of daughters are important parameters that will need to
be modeled.

Waste Form and Containment

Radioactive contaminants are present in a wide variety
of waste forms that influence their mobility.  However,
in most cases, the radionuclides of concern are long-
lived, and the integrity of the waste form or container
cannot be relied upon for long periods of time.
Therefore, the source term is  often conservatively
modeled as a uniform point, areal, or volume source,
and  no  credit  is  taken  for  waste   form  or
containerization (EPA92).

If it is desired to model explicitly the performance of
the waste  form (e.g., rate of degradation of solidified
waste  or  containerized waste) or transport in  a
complex geochemical environment (changing acidity,
presence of chelating agents or organics), complex
geochemical models may be needed.  Depending on
the waste form and container, such models would need
to simulate the degradation rate of concrete, the
corrosion  rate of steel,  and the leaching rate of
radionuclides associated with various waste forms (i.e.,
soil, plastic, paper, wood, spent resin, concrete, glass,
etc.).  These processes depend, in part, on the local
geochemical   setting.   However, it is  generally
acknowledged that it is not within the current state-of-
the-art to explicitly model the geochemical processes
responsible for the degradation of the waste containers
or the waste itself (NRC 90).

Physical and Chemical Properties of the
Radionuclides

If feasible, the conceptual  model  of the site  should
describe the  radionuclides and their physical  and
chemical characteristics.  These parameters may be
pertinent   to   model   selection  because  certain
radionuclides  have  properties  that  are  difficult to
model. For instance, most of the NPL and SDMP sites
are contaminated with thorium and uranium, both of
which decay into multiple daughters which may differ
from their parents both physically and  chemically.
Some of  the  radionuclides (e.g., uranium)  exhibit
complex geochemistry and their mobility is dependent
upon the redox conditions at the site.  Though the
chemical  form  of  the   radionuclides  and  the
geochemical setting can have a profound effect on the
transport  of  the radionuclides,  it  is  generally
acknowledged  reliable  modeling of  the various
geochemical   processes   is  not  often   feasible.
Accordingly,  during  the  construction of a  site
conceptual model, detailed information regarding the
chemical composition of the radionuclides may not be
necessary.    The  degree  to which  this  type  of
information will be  needed to  support  remedial
decision making will surface as site characterization
proceeds.

Geochemical Setting

In addition  to the standard chemical properties of
radionuclides, it is  important to understand the
geochemical properties and processes that may affect
transport of the radionuclides that are specific to the
site.   These properties  and  processes include the
following:

   ! Complexation  of  radionuclides   with  other
     constituents

   ! Phase transformations of the radionuclides

   ! Adsorption and desorption

   ! Radionuclide solubilities at ambient geochemical
     conditions

If it is desired to model these processes explicitly, as
opposed to using simplifying assumptions, such as
default or aggregate retardation coefficients, more
complex   geochemical  models  may  be  needed.
However, as discussed above, it is currently not often
feasible to explicitly  model  complex  geochemical
processes.

3.2.2 Environmental Characteristics

The  conceptual model of the site should begin to
address the complexity of the  environmental  and
hydrogeological setting. A complex setting, such as a
complex lithology, a thick unsaturated zone, and/or
streams or other bodies of water on site (i.e., a complex
site), generally indicates that the direction and velocity
of ground-water flow and radionuclide transport at the
site cannot be reliably simulated using simple one-
dimensional, analytical models (see Appendix C).
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At more complex sites, such as many of the defense
facilities on the NPL, the remedial process is  gener-
ally structured so that, as the investigation proceeds,
additional data become available to support ground-
water modeling.  An understanding of the  physical
system, at least at a sub-regional scale, may  allow an
early determination of the types of models appropriate
for use at the site. Specifically, during the early phases
of the  remedial process, when site-specific data are
limited, the following site  characteristics  may be
extrapolated from regional-scale information and will,
in part, determine the types and complexity of models
required:

   ! Approximate depth to ground water

   ! Ground-water flow patterns

   ! Lithology of the underlying rocks (e.g., limestone,
    basalt, shale)

   ! Presence of surface water bodies

   ! Land surface topography

   ! Sub-regional recharge and discharge  areas

   ! Processes or conditions that vary
    significantly in time

Even at complex sites, complex computer models may
not be needed.    For example,  if a  conservative
approach  is  taken,  where  transport  through the
unsaturated zone is assumed to be instantaneous, then
the  complex  processes associated with flow and
transport through the unsaturated zone would not need
to be  modeled.    Such  an  approach  would be
appropriate at sites that are relatively small and where
the extent of the contamination is well defined.  Under
these conditions, the remedy is likely to be removal of
the contaminated surface and near-surface material.
Examples of these  conditions are many of the SDMP
sites and several of the non-defense NPL sites. In
these cases, the use of conservative screening models,
along with site  data, may be sufficient  to support
remedial decision  making throughout the remedial
process.

Depth to Ground Water

Sites located in the  arid west and southwest (e.g.,
Pantex, Hanford, and INEL) generally have greater
depths to ground water. The simulation of flow and
transport through the unsaturated zone will generally
require more complex computer codes due to the non-
linearity of the governing equations. Modeling of the
unsaturated zone is further hampered because the
necessary data are often difficult to obtain.

Ground-Water Flow Patterns

The intricacy of the ground-water flow patterns will
have a significant  impact  on the complexity of the
required  modeling.   The  dominating factors that
control the flow patterns are both the geology and
hydraulic boundaries. Flow in the saturated zone will
tend to be uniform and  steady in hydrogeologic
systems  that  have uncomplicated  geology  and
boundary conditions that are relatively stable with
time.   Uniform flow refers to flow that is in one
direction and does not vary across the width of the flow
field.   Steady flow does not  change over  time.
Boundary   conditions,   such  as  constant
pumping/injection and recharge from perennial lakes
and streams, are generally constant over time.

Hy drogeological features that indicate that flow may be
unsteady  and nonuniform are  areas where  discrete
geologic  features are known to exist (e.g., faults,
fractures, solution  channels), as  well  as hydraulic
boundaries  which may consist of ephemeral streams,
highly variable rainfall,   and  areas  occasionally
indurated by flooding.

Sub-Regional Lithology

The lithology of the underlying rocks also provides
insight into  the   expected level  of  difficulty of
modeling.  A number of the NPL sites overlie areas
where fractures are probably dominant mechanisms for
flow and transport.  These sites include Hanford, Idaho
National Engineering Laboratory (INEL), Maxey Flats,
Jacksonville, Oak Ridge, West Valley, and Pensacola
Air Stations.  In some cases, such as at Hanford, the
fractured zone is deep  below the site, and concerns
regarding ground-water contamination are  limited
primarily to the near-surface sedimentary rock.
It is unlikely that analytical models could be used to
adequately describe flow and transport in the fractured
systems because radionuclide transport and ground-
water flow in fractured media are much more complex
than in unfractured granular porous media. For that
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matter, it generally requires very specialized numerical
codes to simulate flow  and transport  in  fractured
media.  This is because of the extreme heterogeneity
and anisotropy associated with the fractures.

Surface Water Bodies

Virtually all of the NPL sites and many of the SDMP
sites have surface water bodies at or in the immediate
vicinity of the site.  Bodies of water often have a
significant impact on the ground-water flow and can
seldom  be  neglected in  the modeling analysis.  In
general, analytical models are limited in their ability to
simulate properly the effect that surface water bodies
have on contaminant flow and transport, particularly
if the surface water body behaves episo-dically, such as
tidal or wetland areas.  Several of the NPL sites are
inundated with wetlands, including Oak Ridge, Himco,
and Shpack Landfill. At least two sites, Pensacola and
Jacksonville, are close to estuaries, which suggests that
tidal as well as density-dependent flow and transport
may be significant.

Sub-Regional Topography

The  land surface topography is often overlooked in
developing a site conceptual model  but may be an
important factor in evaluating the  need  for,  and
complexity of, ground-water modeling.  Topography
may  significantly   influence  ground-water  flow
patterns. For instance,  Maxey Flats is situated atop a
relatively steep-sided plateau with a stream located at
the bottom  of the   slope.   The  steep  topo-graphy
strongly controls the direction of ground-water flow,
making it  much more  predictable.   Furthermore,
estimating the flux of ground water moving into the
system from upgradient sources becomes much simpler
if the area of interest is a local recharge area, such as
a hill or mountain.

Steep topography can also complicate the modeling by
making it more  difficult  to simulate hydraulic heads
that  are representative of the hydrologic  units of
interest.

Regional Recharge/Discharge

The ground-water flow paths will largely be controlled
by regional and sub-regional ground-water recharge
and discharge areas. It is generally necessary to ensure
that the conceptual model of flow and transport on a
local scale is  consistent with the sub-regional  and
regional scale.  If the site is located in an aquifer
recharge area, the potential for widespread aquifer
contamination is significantly increased, and reliable
modeling is essential.

3.2.3 Land Use and Demography

The site conceptual  model will need to identify the
locations where ground water is currently being used,
or may be used in the future, as a private or municipal
water supply. At sites with multiple user locations, an
understanding of ground-water flow in two or three
dimensions is needed in order to predict realistically
the likelihood that the contaminated plume will be
captured by the wells located at different directions,
distances,  and depths  relative  to   the sources  of
contamination.

Simple  analytical ground-water flow and transport
models  typically  are  limited  to   estimating  the
radionuclide  concentration in the plume  centerline
downgradient from the source. Accordingly, if it is
assumed that the receptors are located at the plume
centerline,  a simple model may be appropriate. Such
an assumption is often appropriate even if a receptor is
not currently present at the centerline location because
the results are generally conservative. In addition, risk
assessments often postulate that a receptor could be
located  directly downgradient of the source at some
time in the  future.

The need for complex models increases if there are a
number of  public or municipal water supplies  in the
vicinity of  the source. Under these circumstances, it
may be  necessary to  calculate  the  cumulative
population  doses and risks, which requires modeling
the radionuclide concentrations at a number of specific
receptor  locations.  Accordingly,   off-centerline
dispersion modeling may be needed.
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                                             SECTION 4
      CODE SELECTION - RECOGNIZING IMPORTANT MODEL CAPABILITIES
The greatest difficulty facing the investigator during the code selection process is not determining which codes have
specific capabilities, but rather which capabilities are actually required to support remedial decision making during
each remedial phase at a specific site. This section is designed to help the remediation manager and support personnel
recognize the conditions under which specific model features and capabilities are needed to support remedial decision
making.
4.1 INTRODUCTION

The influence that site and code related characteristics
have on code selection can be both global in nature as
well as very specific and exacting. For this reason, this
section is divided into two distinct parts.  The first part
addresses general considerations of the code selection
process.  The discussion provides an overview of how
the code selection  process  is  influenced by  the
interdependency between the modeling objectives and
the site and code characteristics.  The second part of
the section focuses primarily on specific considerations
related to the code selection process.  The discussion
provides the information necessary to determine which
specific  site  characteristics need  to  be  explicitly
modeled and  when attempting  to   model  such
characteristics is impossible, unjustified, or possibly
even detrimental to the modeling exercise.

4.2 GENERAL  CONSIDERATIONS  - CODE
    SELECTION DURING EACH  PHASE  IN
    THE REMEDIAL PROCESS

Successful ground-water modeling must begin with the
selection of a computer code that is not only consistent
with the site characteristics but also with the modeling
objectives, which depend strongly on the stage of the
remedial process; i.e., scoping vs. site characterization
vs. the selection and implementation of a remedy.
There are no fail-safe methods for selecting the most
appropriate computer code(s) to address a particular
problem. However, the entire process of code selection
can be relatively straightforward if it is given adequate
attention early in the project development.

One of the primary goals of mathematical modeling is
to synthesize the conceptual model, as discussed in
section 3, into mathematical expressions, which, in
turn, are solved by selecting an appropriate computer
code.    This section discusses  how the different
components of the conceptual model, in conjunction
with the modeling objectives, influence the modeling
approach and ultimately the selection of the most
appropriate computer code.

The  underlying premise of this section is that the
various aspects of the  conceptual model may  be
simulated in a variety  of ways,  but the selected
approach must remain consistent with the objectives.
That  is, the  physical  system  cannot be  overly
simplified to  meet ambitious objectives,  and less
demanding objectives should not be addressed with
sophisticated models.

Table 4-1 presents an overview of how the overall
approach to modeling a site differs as a function of the
stage of the remedial process. The most common code
selection mistakes are selecting codes that are more
sophisticated than are appropriate  for the available
data or the  level of the  result desired,  and the
application of a code that does not account for the flow
and transport processes that dominate the system. For
example, a typical question that often arises is: when
should three-dimensional codes be used as opposed to
two-dimensional or one-dimensional codes? Inclusion
of the third dimension requires substantially  more data
than one-  and two-  dimensional  codes.    Similar
questions need to be  considered which involve the
underlying assumptions in the selection of a modeling
approach and the  physical processes which are to be
addressed.     If  the  modeler  is  not  practical,
sophisticated codes are used too early in the problem
analysis.  In other instances, the complexity of the
modeling is  commensurate with the qualifications of
the modeler. An inexperienced modeler may take an
unacceptably simplistic approach.
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            Table 4-1.  General Modeling Approach as a Function of Project Phase
Attributes
Accuracy
Temporal Representation of
Flow and Transport Processes
Dimensionality
Boundary and Initial
Conditions
Assumptions Regarding Flow
and Transport Processes
Lithology
Methodology
Data Requirements
Scoping
Conservative
Approximations
Steady-State Flow and
Transport Assumptions
One-Dimensional
Uncomplicated
Boundary and Uniform
Initial Conditions
Simplified Flow and
Transport Processes
Homogeneous/Isotropic
Analytical
Limited
Characterization
Site-Specific
Approximations
Steady-State Flow/Transient
Transport Assumptions
1 ,2-Dimensional/Quasi-
3 -Dimensional
Non-Transient Boundary
and Nonuniform Initial
Conditions
Complex Flow and
Transport Processes
Heterogeneous/Ani so tropic
Semi-Analytical/Numerical
Moderate
Remediation
Remedial Action Specific
Transient Flow and
Transport Assumptions
Fully 3-Dimensional/Quasi-
3 -Dimensional
Transient Boundary and
Nonuniform Initial
Conditions
Specialized Flow and
Transport Processes
Heterogeneous/Ani so tropic
Numerical
Extensive
One should begin with the simplest code that would
satisfy the objectives and progress toward the more
sophisticated codes until the modeling objectives are
achieved.

The remedial process is generally structured in a way
that is consistent with this  philosophy; i.e.,  as the
investigation  proceeds,  additional   data  become
available to support more sophisticated ground-water
modeling.  The data that are available in the early
stage of the remedial process may limit the modeling
to one or two dimensions. In certain cases, this may be
sufficient to support remedial decision making.  If the
modeling objectives cannot  be  met in this manner,
additional data will be needed to support the use of
more complex models. The selection of more complex
models in  the later  phases often depends  on the
modeling results obtained with simpler models during
the early phases.

Generally in the  later phases of the investigation,
sufficient data have been  obtained  to  meet  more
ambitious objectives  through complex three-dimen-
sional modeling.  The necessary degree of sophistica-
tion of the modeling effort can be evaluated in terms of
both site-related issues and objectives, as well as the
qualities inherent in  the  computational methods
available for solving ground-water flow and transport.

Modeling objectives for each stage of the remedial
investigation must be very specific and well  defined
early within the respective phase of the project. All too
often  modeling is performed without developing a
clear rationale to meet the objectives, and only after the
modeling  is completed are the  weaknesses in the
approach discovered.

The modeling  objectives must consider the decisions
that the model results are  intended to support.  The
selected modeling approach should not be driven by
the data availability, but by the modeling objectives
which should  be defined  in terms of what can be
accomplished with the available data. It is important
to keep in mind that the modeling objectives should be
reviewed and  possibly revised during the modeling
process. Furthermore, ground-water modeling should
not be thought of as  a static or linear process, but
rather one that must be   capable of continuously
adapting to reflect changes in modeling  objectives,
data needs, and available data.

A final consideration, true for all phases of the project,
is to select codes that have been accepted by technical
experts and used within a regulatory context.

The  following discusses  computer  code selection
during each phase of the remedial process.  The
emphasis is placed on the processes and assumptions
inherent in the mathematical models used in computer
codes. The discussion is organized according to the
factors delineated in Table 4-1.
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4.2.1    Scoping

In the scoping phase, site-specific information is often
limited. Therefore, the modeling performed during the
early planning phase of most remedial investigations
is generally  designed  to support relatively simple
objectives which can be easily tied to more ambitious
goals developed during the   later  phases  of  the
investigation.  The very nature of the iterative process
of data collection, analysis, and decision making
dictates that the preliminary objectives will need to
evolve to meet the needs of the overall program. That
is, it would be unreasonable to assume that simplified
modeling based upon limited data would do little more
than provide direction for future activities.

An important issue that often arises during the scoping
phase is whether remediation and decommissioning
strategies can be selected during the scoping phase
using limited data and simple screening models. Such
decisions  can be costly at complex  sites where the
nature and extent of the contamination and transport
processes are  poorly  understood.   How-ever, at
relatively simple sites, early remediation decisions can
be made, thereby avoiding the unneces-sary delays and
costs  associated  with  a possibly pro-longed  site
characterization and modeling exercise.

A large  part of code selection in the early phase of the
investigation is understanding  the project  decisions
that need to  be made, and, of these, which can be
assisted through the use  of specific codes under the
constraints of both limited data and an incomplete
understanding  of  the  controlling hydrogeologic
processes at the site.   It is not always necessary to
select a computer code or analytical method that is
consistent with all aspects of the conceptual model. It
is often useful to model only certain components of the
conceptual model. In practice, early modeling focuses
upon assessing the significance  of specific parameter
values and their effects on flow and transport rather
than  modeling  specific  hydrogeologic  transport
processes.  For instance, it is  common during the
scoping phase to evaluate transport as a function of a
range of hydraulic conductivities;  however, it is
unlikely that more complex processes such as flow and
transport through fractures would be considered.

Because general trends, rather than accuracy, are most
important during the scoping phase, a computer code
or analytical method would need to be capable only of
accommodating the following:
     !   Conservative Approximations

     !   Steady-State Assumptions

     !   Restricted Dimensionality

     !   Uncomplicated Boundary and Initial
        Conditions

     !   Simplified Flow and Transport Processes

     !   System Homogeneity

These model attributes generally translate to modeling
approaches that are consistent with the available data
during the scoping phase.  They are discussed in
greater detail in the following sections.

4.2.1.1  Conservative Approximations

In the scoping phase of the investigation, the objectives
are  generally  focused  on  establishing order  of
magnitude estimates of the  extent of contamination
and  the   probable    maximum   radionuclide
concentrations at actual or potential receptor locations.
At most sites, the migration rates and contaminant
concentrations  are  influenced  by  a  number  of
parameters and flow and transport processes which
typically would not have been fully characterized in the
early phase of the investigation.  The  parameters
include  recharge,  hydraulic conductivity, effective
porosity, hydraulic gradient,  distribution coefficients,
aquifer  and confining unit  thicknesses,  and source
concentrations.  Questions  during the early phases
regarding flow and transport processes are typically
limited  to more  general considerations, such as
whether flow and transport are controlled by porous
media  or  fractures  and whether  the wastes  are
undergoing transformations from one phase to another
(e.g., liquid to gas).

One of  the most useful  analyses at this point in the
remedial program is to evaluate the potential effects of
the controlling parameters on flow and transport. One
objective  of the  early   analyses  is  to  assess  the
relationship among the parameters. How do changes
in one parameter affect the others and the outcome of
the modeling exercise? A better understanding of such
interdependencies would assist in properly focusingthe
site characterization activities and ensuring that they
are adequately scoped.  Obviously, it would also be
desirable to evaluate the  effects that various processes
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would have on controlling flow  and  transport;
however, this would generally have to be deferred until
additional   information  is  obtained  during  site
characterization. Furthermore, some caution is needed
in that if simplistic assumptions have been made in the
model, the results may not be valid (i.e., transferable)
to a  more  refined  model  that  incorporates more
realistic  or complex boundary  conditions,  initial
conditions, or parameter variations.

In general, the uncertainty associated with each of the
parameters is expressed by a probability distribution,
which yields  a  likely  range of values  for each
parameter of interest. At this phase in the remedial
process, it is important to select a modeling method
where  individual  parameter   values   can   be
systematically selected from the parameter range and
easily substituted into the governing  mathematical
equations which describe  the dominant flow  and
transport processes at the site.  In this manner, the
effects that a single parameter  or  a multitude of
parameters have on the rate of contaminant movement
and concentrations may be evaluated. This technique
of substituting one  value for another from within a
range of values is called a sensitivity analysis. It is
important to ensure that  the range of individual
parameter values and parameter combinations selected
allow for a conservative  analysis of the flow  and
transport processes.

In many  cases,  the possible range of values of
important parameters is unknown or very large. As a
result, the analyst has little alternative but to evaluate
the sensitivity of the results to a very broad range of
possible values for the parameters.  Many of these
results will be unrealistic but cannot be ruled out until
reliable  site  data  are   obtained  during  site
characterization.  These types of analyses are useful
because they help to direct the field work.  However,
they can also be used incorrectly.  For  example,
individuals not familiar with the scoping process could
come to grossly inappropriate conclusions regarding
the potential public health impacts of the site based on
the results  of scoping analyses.  Accordingly, care
must be taken to assure  that  the results of scoping
analyses are used to support the decisions for which
they were intended.

An alternative to the detailed sensitivity analysis is a
conservative bounding  approach.    In  this  less
demanding  analysis, values  are selected from the
parameter range to provide the highest probability that
the results are conservative, i.e., that the contaminant
migration rates and  concentrations would  not be
underestimated. For example, high values of hydraulic
conductivity combined with low  effective porosities
and distribution coefficients would tend to maximize
the predicted contaminant migration rates although the
concentrations at receptors may be underestimated.

It is important to keep in mind that even though efforts
are made to ensure a conservative analysis, a number
of natural as well as anthropogenic influences may
adversely affect the migration of radionuclides.  For
instance, distribution coefficients that are published in
the literature are frequently determined at neutral pH
values. However, even values conservatively selected
from the low range could be  too  high if acid wastes
have been discarded with the radioactive  material.
Burrowing animals and construction activities have
also been responsible for moving radioactive wastes
beyond the boundaries predicted by ground-water flow
and transport models.

Other  processes  that could render an  otherwise
conservative  analysis  with  erroneously  optimistic
results include  facilitative transport  and  discrete
features,   such as  soil  macropores.   Facilitative
transport is a term used to describe the mechanism by
which radionuclides may couple with either naturally
occurring material or other contaminants and move at
much faster rates than would be predicted by their
respective distribution  coefficients.   Furthermore,
discrete  features  are rarely considered  in  early
analyses, even though it is well  known that discrete
features,   such  as  soil  macropores,  can  allow
contaminant movement on the order of meters per year
in the vadose  zone.   The result could be a gross
underestimate of the time of arrival and concentration
of contaminants downgradient. Nonetheless, the lack
of site-specific data  will generally preclude the
mathematical  modeling  of  anomalous flow  and
transport processes during the project scoping phase.
Therefore,  the potential exists  that   what would
normally be considered conservative modeling results
are actually underestimating the contaminant velocities
and concentrations.  This possibility highlights the
need for confirmation of modeling results with site-
specific field data even if a conservative approach has
been undertaken.

As far as code selection is  concerned, three basic
choices are available:  analytical, semi-analytical, or
numerical codes (Appendix C). Analytical and semi-
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analytical methods, which are limited to simplified
representations of the physical setting and flow and
transport processes, are ideally suited for performing
sensitivity and conservative bounding analyses because
they are  computationally  efficient  (i.e.,  fast) and
require relatively little data as input (Section 4.3.2.1).
Several analytical models are set up specifically for
performing sensitivity analyses.

In contrast, numerical methods do not lend themselves
to the same kind of "simplified" applications.  The
primary reasons are that numerical models are difficult
to set up, require a large amount of data input to
calibrate  the   model,   and  multiple  parameter
substitutions   are  generally   very   cumbersome.
However, the bottom line is that simply not enough
data exist in the early phases of a remedial project to
construct and perform defensible numerical modeling.

4.2.1.2  Steady-State Solutions

In the scoping phase, the data that  are generally
available have been collected over relatively short time
intervals.  Therefore, modeling objectives would be
limited to those which could be met without a detailed
understanding  of the temporal nature of processes
affecting flow and transport.  For example, a typical
analysis that would not require detailed knowledge of
the  temporal nature of recharge, source release rates,
and other flow and transport mechanisms would be the
estimation of the distance that  radionuclides  have
traveled since the beginning of waste management
activities.  This analysis would use yearly average
values for the input parameters,  such as ambient
recharge, stream flow stages, and source concentration
release rates.   However, without accommodating the
transient nature of these processes, predictions of peak
contaminant concentrations arriving at downgradient
receptors would be  associated with a high degree of
uncertainty.

Analytical transport solutions are generally able to
simulate only  systems that assume steady-state flow
conditions, but, because  the available data rarely
support transient  simulations during the scoping
phases, common analytical methods may oftenbe used
more effectively than numerical methods. It is much
easier to conduct bounding and  sensitivity analyses
with analytical rather than numerical models.

4.2.1.3  Restricted Dimensionality
Ground-water flow  and contaminant  transport are
seldom constrained to  one  or  two  dimensions.
However,  during scoping, modeling objectives must
take into  account that there is rarely  sufficient
information to describe mathematically the controlling
flow and transport processes in three dimensions.  In
reality,  most of  the  modeling analysis  in  the
preliminary  investigation will focus upon centerline
plume  concentrations which are essentially one- and
two-dimensional analyses. One-dimensional analyses
of the unsaturated zone are customarily performed in
a cross-sectional orientationbecause flow and transport
are predominantly vertically downward.  Similarly, in
the  saturated zone, vertical gradients  are generally
much smaller than lateral gradients and, as a result,
vertical transport  need not  always   be  explicitly
modeled.  Therefore, two-dimensional areal analyses
may be appropriate.

Figures 4-1 through 4-4 may be useful  in visualizing
the   differences  between one-,  two-, and three-
dimensional modeling.  In one-dimensional modeling,
the  radionuclide  concentration is predicted in the
plume centerline in the x direction, and no information
is provided on the radionuclide concentration in the y
or z direction (Figure 4-1).
Figure 4-1.   One-Dimensional Representation of
             Conceptual Model
                                                   4-5

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In two-dimensional cross-sectional models for the
unsaturated zone, the radionuclide concentration is
calculated for the x and z direction and it is assumed
to be the same at any slice through the plume in the y
direction (Figure 4-2).
Figure 4-2.  Two-Dimensional Cross-Sectional
            Representation of Unsaturated Zone in
            Conceptual Model

In saturated zone area!  models, the radionuclide
concentrations are predicted for the x andy directions,
but it is assumed the radionuclide concentration is the
same in any  slice  in  the z direction (i.e.,  the
concentration at any location is the same at all depths)
(Figure 4-3).
                X^         -^"
            / •"  /      ^^if J..-"'
            '    i     ,-"  ~sy
              rVrV-^
Figure 4-3.  Two-Dimensional Area!
            Representation of Saturated Zone
            Conceptual Model

Cross-sectional modeling of the saturated zone  in
which flow is assumed to be in the lateral and vertical
directions (e.g., transverse flow is ignored) may also be
performed.    A  quasi-three-dimensional  modeling
approach  is  also  commonly  used  when  vertical
components of flow  within aquifers  are  deemed
unimportant.  This  approach assumes that  ground-
water flow  through any confining units that  separate
aquifers  is in only one  dimension (i.e., vertical).
Furthermore,  flow  within  the  aquifers  is  two
dimensional (i.e., vertical flow component is ignored).
In  this  manner,  the  effects of the  hydraulic
interconnection  among interbedded aquifers  and
confining units canbe simulated without having to rely
on fully three-dimensional models.

Three-dimensional  models   will  calculate   the
radionuclide concentrations at any x, y, z coordinate,
taking into  consideration the variations  in  the
lithography and  hydrogeology in  three dimensions
(Figure 4-4).
        v
        ,.-•"
            \-S//t
               ..'**'     •    f
             X ^    /   /
                .«".    _x
 i        ^ $\S   /
  ••-*.   -.-'      * --x^
***4* "S°"x.^'"""     ,,-f* "%    ./  ;
    ••^       «•  ?  *
Figure 4-4.  Three-Dimensional Representation of
            Conceptual Model

A typical three-dimensional problem would be one
which would be designed to evaluate the geometry of
hypothetical capture zones if one or more extraction
wells were planned for the remediation of the ground
water. The vertical ground-water gradient that would
be artificially created by the pumping wells, as well as
the induced vertical leakage from overlying and
underlying  hydrogeologic units,   would be  very
important to consider in this analysis. If this leakage
were  not accounted for,  the  effectiveness of  the
remedial system would be substantially overestimated
                                                  4-6

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because the radii of the capture zones would be too
large.

As a general rule, analytical methods, which can be
performed on a hand-held calculator, are developed for
predicting concentrations along the centerline of the
plume and are limited to  one dimension.  Two- and
three-dimensional analyses are customarily performed
with the assistance of a digital computer. Although
analytical solutions are available for two- and three-
dimensional analysis, the limitations that are placed
upon the solution techniques are so severe that they
can be used only to simulate gross system behavior.
Therefore, the three-dimensional example provided
above could not be  satisfactorily  addressed  by an
analytical model because of computational limitations,
such as  simple boundary  conditions and  uniform
geology.    However,  attempts to circumvent the
limitations of analytical  methods  at this phase by
adopting numerical methods would only complicate
the problem for reasons previously discussed, as well
as now having to provide parameter estimates in the
second or third dimension.

At this phase, the question is not really whether to use
analytical or numerical  methods but rather how many
dimensions should be included in the analytical
                          modeling. The advantages of adding a second or third
                          dimension  must be carefully  weighed against the
                          further complications  of performing the  sensitivity
                          analysis which provides the real strength behind the
                          application of analytical methods.

                          4.2.1.4  Uncomplicated  Boundary  and  Uniform
                                  Initial Conditions

                          Boundary conditions are the conditions the modeler
                          specifies as known values in  order to solve for the
                          unknowns  in  the  problem domain (Figure 4-5).
                          Ground-water boundaries may be described in terms of
                          where water is flowing into  the ground-water system
                          and where water is  flowing out. Many different types
                          of boundaries exist, including:  surface water bodies,
                          ground-water divides,  rainfall, wells, and geologic
                          features such as faults and sharp contrasts in lithology.
                          Initial conditions are defined as values of ground-water
                          elevation,   flow   volumes,   or  contaminant
                          concentrations which  are initially  assumed  to be
                          present in the area of interest.

                          Governing equations that describe ground-water flow
                          and contaminant transport and associated boundary
                          and initial conditions may be solved either analytically
                          or numerically.  Analytical solutions are  preferable
                          because they are easily  adapted to sensitivity analyses;
                          however, in most cases, analytical methods are not
                          possible because of irregularly shaped boundaries and
                          heterogeneity of
                               Ji
^   \   v-,,7;;
^^A^f^-x
                                                                  f/   •-

                                                                 , f  ' t*iir-'
                                                                ff
                                                                "• I
                                f    t    1
Figure 4-5.   Typical System Boundary Conditions
                                                  4-7

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both the geology and flow field.  If very few data are
available for the site, it would be very unlikely that
reliable ground-water elevations and flow volumes
could be assigned to calculate the unknowns in the
domain of a  numerical model.   Furthermore,  the
boundary conditions in the numerical model are not
supposed to be subject to radical adjustments and are
generally excluded from detailed sensitivity analyses.
In contrast to numerical methods, analytical methods
are conducive to  testing and  evaluating  both  the
boundary and initial conditions.  In fact, analytical
methods do not require that boundary values be known
and assigned for the planes and surfaces that surround
the modeled region. However, this is also a limitation
of analytical methods in that, if boundary conditions
vary within the problem domain, they cannot  be
adequately simulated.

The lack of site-specific data available in the scoping
phase will generally not allow a good definition of the
system boundary and initial conditions; therefore, the
objectives will be confined to very limited calculations
of approximate travel  distances  and  contaminant
concentrations.

Most analytical models will not accommodate non-
uniform boundary or initial conditions. Therefore, if
the domain includes areas where recharge is variable
or a lake or stream exhibits strong effects on the flow
field, analytical modeling  will not  provide  good
agreement with the overall system behavior. It follows
that, if the flow field is uniform, which can generally
be described with simple uniform boundary conditions,
analytical models provide a better method for testing
the boundary conditions than do numerical methods.
However, the  true  nature of the flow field cannot be
determined until the site is characterized.

4.2.1.5  Simplified Flow and Transport Processes

Site-specific  information describing  the flow and
transport processes which dominate the migration of
radionuclides  would not be available before detailed
site   characterization   activities   are   conducted.
Therefore,  modeling  objectives would need to  be
defined as  those that could be addressed with only
limited knowledge of  the  site hydrogeology and
geochemistry.   In practice, this means that uniform
porous media flow would be assumed, and that all of
the geochemical reactions that affect the radionuclide
transport would  be lumped together  as  a single
parameter   termed  the  distribution   coefficient.
However, the effects of dilution due to the lateral
spreading of the plume over a uniform flow field can
be considered as well as the radionuclide half-lives.

Discrete features, such as macropores, fractures, and
faults, would generally have to be neglected for the
flow   and  transport  analysis,   and  distribution
coefficients would be selected from literature values
judged to be conservative.  Movement through the
unsaturated zone would be simulated with simplified
versions of more complex equations describing the
unsaturated flow and transport.

Unless there were sufficient data to  prove to the
contrary, it would be assumed that the flow field was
uniform,  and,  at  this time,  there  would  be few
advantages to selecting a numerical model  over an
analytical one.  Analytical  methods do  exist that
describe the flow  and  transport of  radionuclides
through fractures.   However,   the  fracture-flow
modeling would have to be performed as a sensitivity
analysis, as the information to adequately describe the
geometry of the fractures would seldom be available
before site characterization.

4.2.1.6  Uniform Properties

Homogeneity  describes a system where  all of the
characteristics are uniform within the aquifer,  whereas
isotropy means that the hydraulic properties are
identical in all directions. A homogeneous system may
have anisotropic flow properties, if, for example, an
otherwise  homogeneous  sandstone  aquifer has  a
greater  hydraulic  conductivity  in  the  horizontal
direction  than  in  the   vertical.     Therefore,
hydrogeologic units may have anisotropic qualities but
still be considered uniform throughout, provided the
anisotropy does not vary within the unit.

Prior to  site  characterization, only the most general
assumptions may be made regarding the relative flow
properties of the aquifers. For example, as a rule of
thumb,  it is  often  assumed  that the  hydraulic
conductivity  in the horizontal direction is ten times
greater  than that in  the   vertical  direction for
sedimentary deposits.

Except for some radial  flow problems, almost  all
available analytical solutions belong to systems having
a uniform steady flow. This means that the magnitude
and direction of velocity throughout the system are
invariable  with respect  to  time  and space, which
                                                   4-8

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requires the system to be homogeneous and isotropic
with respect to thickness and hydraulic conductivity.
Therefore,  analytical methods will not allow  the
simulation of flow and transport through layers of
aquifers and  aquitards.   Furthermore, if there is a
divergence from these uniform properties within the
aquifer, such as direction flow properties of buried
stream channels, analytical models would be unable to
simulate the effect that these features would have on
flow and transport.  However, it is unlikely that this
detailed information would be available prior to the
site characterization program.

4.2.2   Site Characterization

The primary reasons for ground-water modeling in the
site characterization phase of the remedial process are
to: (1) refine the existing site-conceptual model; (2)
optimize the effectiveness of the  site characterization
program; (3) support the baseline risk assessment; and
(4)  provide  preliminary  input  into the  remedial
approach.   To accomplish these goals, it is generally
necessary  to apply relatively complex ground-water
models to simulate flow and transport in the saturated
zone and, in many instances, the unsaturated zone.

A properly designed site characterization program will
expand the data base to enable very specific and often
demanding objectives to be addressed. To meet the
more rigorous requirements, the simplified modeling
approaches undertaken in the scoping phase give way
to more sophisticated  means of  data evaluation.
However,  this added  sophistication and heightened
expectations also convey far more  complications in
selecting the proper modeling approach. As discussed
previously, the two general types of modeling options
that could be selected during the site characterization
program include analytical and numerical modeling
methods.

In  many   instances,  several  different  modeling
approaches will be taken to accomplish the objectives
at a particular phase in the investigation. For example,
the  output of analytical modeling of the unsaturated
zone, in the form of radionuclide concentrations at the
interface between the saturated and unsaturated zone,
may be used as input to numerical models  of the
saturated zone.  It must always be kept in mind that,
regardless of the phase of the remedial process, the
simplest modeling approach that meets the modeling
objectives should be taken.
The site characterization program is the first time in
the investigation where flow and transport processes
are identified  and  investigated.   Prior  to  site
characterization activities, the investigator could only
evaluate the effects of various parametervalues onflow
and transport.  In the scoping phase, the modeling
focuses on parameter estimations rather than on the
effects that geochemical and physical flow mechanisms
could have on the fate and transport of contaminants.
Examples  of these mechanisms  include processes
related  to  fractures,  density dependence,  phase
transformations, and  changes in the  geochemical
environment.

It is important during the site characterization to gain
an  appreciation  for the  governing  geochemical
processes, as these reactions may have a significant
impact on the transport of contaminants  and can be
simulated indirectly  in the analysis by assuming  a
specified amount of contaminant retardation.  Direct
means (computer codes) for simulating geochemical
processes are available; however, a detailed discussion
of these methods is beyond the scope of this report.

As additional  data  are acquired during the site
characterization program and abetterunderstanding of
the hydrogeology is achieved, the modeling approach
and code selectionbecome more involved. Without the
data limitations that constrained the choice of methods
to  those of an analytical nature in the scoping phase,
the number of possible alternatives in the modeling
approach   and  code  selection   process increases
significantly.

Rather than examine many of the available computer
codes and their inherent limitations and capabilities,
the following discussion addresses the rationale for
adopting a modeling approach that will be consistent
with the objectives.  This is important because it is
relatively easy to determine the various attributes of the
existing computer codes; however,  it is far more
difficult to understand the relevance of these attributes
as they apply to a specific site  and the modeling
objectives.
The following subcategories, keyed to Table 4-1, are
analogous to those presented in the scoping phase.
Because  the  modeling  objectives   of  the   site
characterization phase differ from those of the scoping
phase, the  approach to modeling is  also different.
                                                   4-9

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Basically, analytical methods will  be replaced by
numerical methods in order to use less restrictive and
more realistic assumptions. The following discussions
provide an overview of the concepts, terminology, and
thought processes necessary to facilitate the model and
computer code  selection process.   The  modeling
approach in the site characterization program will
generally be based upon the following:

     !    Site-Specific Approximations

     !    Steady-State Flow/Transient Transport

     !   Multi-Dimensional

     !    Constant Boundary and Non-uniform Initial
         Conditions

     !    Complex Flow and Transport Processes

     !    System Heterogeneity

Obviously, if  the  site  characterization  activities
discover  that  the  system  is very  simple  and the
objectives can be addressed with analytical modeling,
an approach similar to that outlined in the scoping
phase can be taken.

4.2.2.1   Site-Specific Approximations

In the scoping phase of the  investigation,  the data
limitations impose  a simple  modeling  approach
which uses conservative parameter estimates. One of
the primary objectives of the  site  characterization
program  is to  obtain sufficient data to enable the
conservative modeling approach to be replaced by a
defensible  and more  realistic  approach  which
incorporates site-specific data.

Many  of the  objectives  defined  for  the  site
characterization phase of the investigation cannot be
met  solely with conservative analyses.  If parameter
values are not known, it  may be  necessary to make
conservative estimates; however, the implications that
a conservative approach may have on other aspects of
the remedial program must also be considered.  For
example, if,  during the  baseline risk  assessment,
conservatively high hydraulic conductivities are used
in order to ensure that the downgradient contaminant
arrival times are not underestimated, several problems
may  occur. First, it would be difficult to calibrate the
model to known parameters (e.g., potentiometric
surface), and adjustments to other parameters wouldbe
required in order to match measured field values. The
end  result would be  a model  that poorly predicts
system responses to hydraulic stresses (e.g., extraction
wells). A second problem would involve contaminant
concentrations. A conservative  increase in hydraulic
conductivity would predict more ground-water flow
through the system than is actually occurring and may
underestimate the  contaminant concentrations  at
downgradient receptors. Furthermore, problems may
arise during the remedial design.   If the modeling
results are used to estimate clean-up times, the model
may predict that water and contaminants are flowing
faster  than  they  actually   are   and  at  lower
concentrations. This would result in an underestimate
of both the amount of time required for remediation as
well as the contaminant breakthrough concentrations.

The  major impact that the formulation  of a more
specific  site-conceptual model will  have on  the
modeling approach is that now parameter ranges have
been narrowed by additional data  acquisition, and
sensitivity analyses can become more focused. This
parameter value refinement diminishes the need to
perform  a multitude  of  sensitivity analyses.   In
conjunction  with  the  increased demand  to  more
accurately simulate the controlling flow and transport
processes, the primary advantages of analytical models
are superseded by their inability to simulate more
complex conditions.  Therefore, the model  selection
process is reduced to determining  which numerical
model will best suit the objectives.

4.2.2.2  Steady-State Flow/Transient Transport

The  data obtained  during the  site  characterization
program are generally collected over relatively short
time intervals  and frequently  do  not  reflect  the
temporal  nature   of  the hydrogeologic  system.
Unfortunately, objectives that need to  be addressed
during the site characterization phase often involve the
prediction of temporal trends in the data. For instance,
the  risk  assessment  would  generally include  an
analysis of the peak arrival times of radionuclides at
downgradient receptors. This incompatibility between
the objectives and data availability gives rise to some
of the greatest uncertainties associated with the entire
remedial investigation.  However, one of the principal
utilities of mathematical models is their ability to
extrapolate unknown values through time.
                                                  4-10

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The modeling approach during site characterization
will generally assume a steady-state flow field and
accommodate  the  transient nature of  the  system
through the contaminant transport analysis. Steady or
transient leaching rates would be used in conjunction
with the existing  plume  concentrations for initial
conditions. Therefore, the system is actually modeled
as a steady flow system and possibly a transient or
pulse-like source term. However, the transient nature
of the plume is generally used as a model calibration
parameter  and  is  not  carried forward into  the
predictive   analysis  for   future  radionuclide
concentrations. That is, rarely are there sufficient data
to describe the temporal nature of the source release.
Exceptions to this  are when records are available
pertaining to the volumes  of radioactive liquids that
were dumped over time into absorption trenches or
when correlations between rainfall events and source
leaching rates may be extrapolated.

Analytical methods are able only to simulate systems
that assume steady-state flow conditions, although
some analytical codes will allow for the simulation of
a transient source term. Therefore, analytical methods
can be used to simulate the temporal nature of  the
contaminant plumes to predict probable maximum
concentrations  and  contaminant  arrival   times.
However, other limitations within the analytical codes
often preclude their use during the site characterization
phase.

Almost all of the numerical transport codes written for
radioactive constituents are able to simulate constant
radionuclide  source  terms with radioactive  decay.
However, if the simulation of a pulse-like source term
is desired, special care is needed to ensure that this
capability has been written into the code.  Otherwise,
the source  release  would  have  to  be  manually
simulated using a code that models a single pulse in an
iterative fashion for each separate pulse.
4.2.2.3  Multi-Dimensional

The site characterization program should be designed
to gather sufficient data to develop a three-dimensional
conceptual model.    It  is  only  after the  three-
dimensional system is relatively well understood that
it can be  determined whether one-, two-, or three-
dimensional modeling is necessary.  If one or two
dimensions are eliminated from the analysis, careful
consideration  needs to be  given to what impact
restricting the dimensions will have on the model's
capability to simulate existing field conditions.

The magnitude of flow and transport in any direction
relative to the other directions provides the rationale
for  which  dimension(s)  should  be  included or
excluded.  In most instances, flow and transport in the
unsaturated zone are assumed to be predominantly
downward with smaller horizontal components. If the
flow components are found to have two dominant flow
directions, a two-dimensional cross section may allow
a representation of the flow field.

Modeling and field validation studies of the vadose
zone (the unsaturated zone) have yielded mixed results
both in model calibration and in  the comparison of
transport predictions against measured field values. In
modeling  the vadose zone, as well as the saturated
zone, the question is always how much uncertainty in
the results is acceptable to meet the objectives.

Two-dimensional simulations of the saturated zone are
usually   performed   when   the   horizontal  flow
components are far greater than the vertical flow
components, allowing the vertical components to be
ignored.  However, much of the modeling performed
for site characterization will be on a scale where the
vertical  components of flow are  usually important
because many natural features, such as surface water
bodies, often have strong vertical flow components
associated with them.  Furthermore, particular  care
must be  taken in eliminating the third  dimension
because  attempts  to  simulate  three-dimensional
processes in two dimensions can lead to difficulties in
model calibration as well as in producing defensible
modeling results.

Water-level data collected from closely  spaced wells
that penetrate the same aquifer at different depths
provide excellent information on the vertical gradients.
This  information may be  used during  the  site
characterization program to  determine  the effective
                                                  4-11

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hydraulic basement of any contamination present, as
well as recharge and discharge areas.  If there are
strong vertical gradients, the capability to simulate the
vertical movement  of ground  water  within the
hydrogeologic system  becomes  very important in
defining the  nature and extent of the contaminant
plume.

It should also be kept in mind that two-dimensional
planar  modeling  will average  the  contaminant
concentrations over the  entire thickness of the aquifer,
and the vertical definition of the contaminant plumes
will be lost. This vertical averaging of contaminants
will result in lower downgradient concentrations and
may not support a base-line risk assessment. Again,
this example illustrates that the decision on how many
dimensions to include in the  modeling must be tied
back to the objectives and the  need to be aware of the
limitations imposed upon the results if one or more
dimensions are eliminated.

The recent development of more sophisticated pre- and
post-processors greatly facilitate  data  entry  and
processing. These  advances, in conjunction with the
rapid increase in computer speeds over the past several
years,  have greatly  reduced  the  time involved in
performing three-dimensional modeling.  In general,
there   are  far  more   concerns   associated  with
constraining  the analysis  to  two  dimensions than
including the third dimension, even if many  of the
parameters in  the third  dimension  have  to  be
estimated.

Two-dimensional   analyses  during  the   site
characterization program are  most valuable for
modeling the unsaturated  zone and  for performing
sensitivity analyses of selected cross-sections through
a  three-dimensional   model.    Two-dimensional
approaches are also useful for performing regional
modeling from which the boundary conditions for a
more site-scale modeling study may be extrapolated.

The objectives for most characterization programs will
be met only by modeling approaches and models that
are multi-dimensional. Analytical models do exist that
are two- and three-dimensional, but  they have very
little versatility and would rarely suffice  in meeting
complicated objectives.  Furthermore, the likelihood
that analytical methods could be effectively used in the
remedial design and evaluation are even more remote.
Therefore, numerical methods should almost always be
chosen if detailed analysis is required to meet the site
characterization objectives.

There are numerous two- and three-dimensional flow
and transport codes to describe  the saturated zone.
However, only a handful of three-dimensional codes
exist that describe flow and transport through the
unsaturated zone. A number of  codes exist that are
generally   three-dimensional;   however,   certain
transport properties (e.g.,  dispersion)  within these
codes are simulated in only  two dimensions.  Special
attention should be given to ensure that the controlling
flow and transport  processes  are  described in the
number of dimensions desired to meet the objectives.

Code selection should not only take into account the
required dimensionality of the site characterization
analysis, but also the projected modeling needs of the
remedial design and evaluation  phase.  It is much
easier to use a code with three-dimensional capability
for a two-dimensional analysis and later expand to the
third dimension than it is to set up a three-dimensional
code  from output obtained from a separate  two-
dimensional model.

4.2.2.4  Constant  Boundary   and  Non-uniform
        Initial Conditions

In  general,   boundary  conditions  are known  or
estimated values  that are assigned to  surfaces  and
planes that either frame the  perimeter of the modeled
area  or  define the  nature  of release  from  the
contaminant  source.  The  different types  of flow
boundary conditions are:  (a) head (ground-water
elevation) is known for surfaces or planes bounding the
modeled region; (b) ground-water flow volumes are
known for surfaces or planes  bounding the modeled
region; (c) some combination of (a) and (b) is known
for surfaces or planes bounding the region. Boundary
conditions could also be assigned to interior features of
the modeled region where ground-water elevations or
flow volumes are known,  such  as lakes, rivers or
marshes.

The most common contaminant-source type boundaries
either specify the source concentration or prescribe the
mass flux of contamination  entering the system. The
concentration is generally prescribed when the release
rate is largely controlled by the solubility limits of the
contaminant. The mass flux type boundary is typically
used when a leaching rate is known or estimated.
Specialized   source  boundaries  have  also been
                                                  4-12

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formulated which allow the source to radioactively
decay. The ability of the code to treat source decay
may not be important if the parents and daughters have
a relatively long half-life when compared to  the
expected travel time to the nearest receptor.

One  of  the  primary   objectives  of  the   site
characterization program is to identify the presence
and location of ground-water flow and contaminant
source boundaries so that they may be incorporated
into the  conceptual model.   These  boundaries  are
generally quantified in terms of the volume of ground
water and contamination moving through the system.
The physical  boundaries are then  translated into
mathematical terms as input into the computer model.

Initial conditions are defined as values of ground-water
elevation,   flow   volumes   or   contaminant
concentrations, which are initially assigned to interior
areas of the modeled regions.  At least for the flow
modeling performed during the site characterization,
the initial conditions are generally  set to uniform
values. This is because the temporal nature of the flow
system is usually  poorly defined.  In addition,  if the
flow analysis is performed to steady-state, which is
usually the case, the initial conditions assigned to the
model domain are irrelevant as identical solutions will
be reached for these values regardless of the values
initially assigned. This occurs because these steady-
state  values  are  solely  dependent  on the values
assigned to the boundaries of the model.

Non-uniform  initial   values   (i.e.,  contaminant
concentrations) are routinely used in the contaminant
transport analysis to depict the geometry and varying
contaminant concentrations within plume, as well as to
define the contaminant concentrations leaching from
the contaminant source. The ability of a code to allow
non-uniform initial conditions would be essential to
fully  describing  and simulating  the contaminant
plume(s).

Analytical  models  are  written  for  very  specific
boundary conditions and uniform initial conditions. In
essence,  this  means that the  boundary  conditions
cannot vary spatially and, in most instances, only one
type of boundary condition can be accommodated.
Furthermore, analytical methods do not allow for the
contaminant source concentrations to change through
time and the measured plume values (i.e., non-uniform
initial conditions) cannot be input  directly to  the
model.   Understandably, these restrictions  would
impose significant limitations on analyzing the data
collected during the site characterization program.

Numerical models are broadly designed to adapt to
many different types  of boundary geometries and
initial conditions. Non-uniform initial conditions for
a single  contaminant plume  can almost always be
varied spatially, depending upon the dimensionality of
the code.

The  ability of numerical models to handle complex
boundaries and non-uniform initial conditions bestow
a versatility to the analysis which should be compatible
with the objectives. This approach is consistent with
the principles behind coupling the sophistication of the
modeling with that of the existing knowledge base.

4.2.2.5  Complex Flow and Transport Processes

Site-specific information describing  the  flow and
transport processes which dominate the migration of
radionuclides would not have been available during the
scoping phase  of the  investigation.   As the site
characterization activities progress, greater attention is
focused upon the physical,  chemical,  and  biological
processes that are affecting ground-water flow and
contaminant  transport.  Up until  this  time,  the
attention has been placed primarily upon estimating
parameter ranges and variances within these  ranges
via the  sensitivity analyses.  This  approach has
limitations and needs to be broadened during the site
characterization phase if  ground-water  flow and
contaminant transport are to be well described. The
means by which this  parameter-based approach is
expanded  is   by  using   computer  codes  that
mathematically accommodate the dominant flow and
transport processes.  These processes could include
flow and transport through fractures,  density-driven
flow, matrix diffusion, fingering, surface water/ground
water interactions,  and geochemical  reactions.  If
present, each of these processes can invalidate the
output of models that are based on the assumption that
uniform flow and transport are occurring  through a
homogenous porous media.

It is  still  likely that all of the geochemical reactions
that affect the radionuclide transport would be lumped
together  into   the  single  parameter  termed  the
distribution coefficient.  However, a better delineation
of any  geochemical   facies  would allow for  the
distribution coefficient to vary from layer to layer as
well as within the units themselves.  If this  simplified
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means of simulating geochemical processes is found to
be  inadequate,  it  may  be  necessary to  utilize
geochemical  models in order to explicitly address
specific  geochemical  reactions  by  relying  upon
thermodynamically based geochemical models.

Movement through the unsaturated zone  could  be
simulated in  a number of different ways depending
upon the objectives.   If the  unsaturated zone is
relatively thin and travel times are short, it may be that
simplified  versions of  more complex  equations
describing the unsaturated flow and transport would
suffice.   However, if the travel time  through the
unsaturated zone is  significant and accurate flow and
transport predictions are required, then mathematical
methods,  which  account  for complex  processes
associated  with  flow and  transport  through  the
unsaturated zone,  may be necessary.

The modeling obj ectives need to be defined prior to the
characterization; only in this fashion can it be assured
that data are sufficient to perform modeling at the
necessary level  of complexity.    All  too  often,
limitations within the data, rather than the modeling
objectives, drive the sophistication of the modeling.

Analytical methods are not well  suited to simulate
complex flow and transport processes. Further, even
numerical methods do not satisfactorily describe some
flow and transport processes.  These processes include
facilitative transport and non-Darcian flow, which are
discussed in section 4.3.

4.2.2.6  System Heterogeneity

One  of  the  primary   objectives  of   the   site
characterization program is to identify heterogeneity
within the system and to delineate  zones of varying
hydraulic properties. System heterogeneity is one of
the leading causes  of a poor understanding of the
physical system controlling flow and transport.

If the accurate simulation of heterogeneous rocks is
required to meet the modeling objectives, analytical
methods would be inappropriate as they assume the
rocks to all have the same properties. In contrast, most
numerical codes allow for zones with different porous
rock properties; however, relatively few codes  can
simulate discrete  features, such as  faults, fractures,
solution features,  or macropores.  Numerical codes
vary from one another in their ability to simulate sharp
contrasts in rock properties. For example, many codes
would have a problem arriving at a solution  (i.e.,
convergence) if very impermeable rocks dissected
highly permeable rocks.   Therefore, if the site was
situated in an alluvial flood plane bordered by low
permeability bedrock, special care would be needed to
select a code that will not have numerical convergence
problems caused by permeability contrasts.

In selecting a computer code to be applied during the
site characterization, consideration should  also be
given to what scenarios may  be modeled during the
remedial investigation.  If a low-permeability slurry
wall or sheet pile  cut-off walls  may be installed, it
would be important that the computer code be able to
simulate these features through permeability contrasts.

4.2.3    Remedial Phase

As the site investigation proceeds  into the remedial
phase, data  are  acquired that will  assist in  the
identification of feasible remedial alternatives. These
data, in combination with models, are used to simulate
the flow and transport in support of the selection,
design,   and   implementation  of  the   remedial
alternatives. The data and models are used to predict
the behavior of ground-water flow and the transport of
radionuclides and  thereby aid in the selection and
design of the remedy and demonstrate that the selected
remedy will achieve the remedial goals.

The  modeling  objectives associated with  remedial
alternative design are generally more ambitious than
those associated with the site characterization phase of
the remedial process.  Therefore, it is often necessary
either to select a computer code with more advanced
capabilities, or modify the existing model in order to
simulate the more complex conditions inherent in the
remedial design. The following are specific examples
of processes that may not be important to the baseline
risk assessment and site characterization, but are often
essential to the remedial design:

    !   three-dimensional flow and transport;

    !   matrix diffusion (pump and treat);

    !   desaturation and resaturation of the aquifer
        (pump and treat);

    !   heat-energy transfer (in-situ vitrification/
        freezing);

    !   sharp contrasts in hydraulic conductivity
        (barrier walls);
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I
    multiple aquifers (barrier walls);
i
    !   the capability  to  move from confined to
        unconfined conditions (pump and treat); and

        ability to simulate  complex flow conditions
        (pumping wells, trenches, injection wells).

From a modeling standpoint, the remedial design is the
most challenging phase of the remedial investigation.
Frequently,  it is the first time in the process  that
sufficient  data are  available to enable the  model
predictions to be verified. The very nature of many of
the potential remedial actions (e.g., pump and treat)
provide excellent information on the temporal response
of the flow and transport to hydraulic  stresses.  These
data allow continuous refinement to the calibration and
enable  the  model  to  become  a   very  powerful
management tool.

The following describes modeling during the remedial
phase of the investigation.  The modeling approaches
taken at  various sites  would generally  have the
following characteristics in common:

    !   Remedial Action Specific

    !   Transient Flow and Transport

    !   Multi-Dimensional

    !   Prescribed Boundary and Non-uniform
        Initial Conditions

    !   Specialized Flow and Transport Processes

    !   System Heterogeneity

4.2.3.1  Remedial Action Specific

As the site characterization process comes to an end
and the Remedial Design and  Selection Phase  is
entered, data have been acquired which will define the
remedial  alternatives.     The  various  remedial
alternatives can be conveniently grouped  into the
following three categories:

    !   Immobilization

    !   Isolation

    !   Removal
This section briefly describes each category, the types
of processes that need to be modeled to support each
category, and the special information needs for each of
these categories. The information is required not only
for implementation of the remedial design but also to
evaluate its effectiveness through numerical modeling.

Immobilization

Immobilization of the radioactive wastes refers to
physical, chemical, and/or biological processes used to
stabilize the radionuclides and preclude their transport.
A number of treatment options exist, each having their
own associated modeling needs, including:

     !   Physical
            vapor extraction
            in-situ coating
            grouting of fissures and pores
        •   in-situ freezing
            in-situ vitrification

     !   Chemical
            induce secondary mineralization
            induce complexation
            alter oxidation-reduction potential

     !   Biotic
            in-situ microbial activity

     !   Physical/Chemical
            alter surface tension relationships
            alter surface charges
            in-situ binding
            adsorbent injection
            radionuclide particle size augmentation
            through clay flocculation

The following  are the types of physical, chemical, and
biological processes that may need to be modeled to
support alternative remedies based on immobilization:

     !   Physical Properties and Processes
            unsaturated zone flow and transport
            heat energy transfer
            multiple layers
            vapor transport
            extreme heterogeneity
            temperature-dependent flow and
            transport

     !   Chemical Properties and Processes
            density-dependent flow and transport
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             oxidation-reduction reactions
             system thermodynamics
             chemical speciation
             ion-exchange phenomena
             precipitation
             natural colloidal formation
             radiolysis
             organic complexation
        •    anion exclusion

     !   Biotic Properties and Processes
             biofixation

It would be  ideal if these processes and properties
could  be  reliably  described  and  modeled  with
conventional and available models. However, many of
these properties and processes are not well understood,
and, in these  instances, models do not exist that yield
reliable results.

The specialized data required to support ground-water
modeling of immobilization techniques include:

     !   Determination of temperature-dependent
        flow and transport parameters

     !   Characterization of geochemical
        environment

     !   Determination of  the  alteration  of  the
        physical rock properties that govern flow and
        transport

     !   Characterization of the microbial
        environment
Isolation

A common  remedial  alternative  is  to  emplace
protective barriers  either to prevent contaminated
ground  water  from  migrating  away  from   a
contaminated site or to divert incoming (i.e., clean)
ground water  from  the  source of  contaminants.
Several types of materials are being used to construct
suchbarriers, including soil andbentonite, cement and
bentonite, concrete, and sheet piling.  An alternative to
the physical emplacement of protective barriers is the
use  of  hydraulic  containment  which  involves
controlling the hydraulic gradient through the use of
injection and/or withdrawal wells or trenches in order
to contain and treat the contaminant plume. Examples
of potential barriers include the following:

     !   Physical
             hydraulic containment
             grout  curtains,  sheet piling, bentonite
             slurry walls
             low  permeability  caps  (clay  and/or
             synthetic)

     !   Chemical
             ion-exchange barriers

     !   Biotic
             microbial barriers

If properly designed and emplaced, such barriers can
last  for  several decades, barring any  geological
disturbances,  such  as   tremors,  ground settling,
significant  changes  in  hydraulic  gradients,   etc.
Accordingly, suchbarriers can be useful in mitigating
the impacts of relatively short-lived radionuclides, or
to control the migration of long-lived  radionuclides
until a more permanent remedy can be implemented.

Several mechanisms or processes can affect the long-
term integrity of such barriers. Once the installation
is complete,  failures  can  be   due  to cracking,
hydrofracturing, tunnelling and piping, and chemical
disruption.   Changes in  the site's  geological or
hydrological   characteristics  can   also  lead  to
catastrophic failures, such as partial collapse, settling,
and  breaking.   If  a  barrier should fail following
installation,   water may   infiltrate  the  site,   and
contaminated leachates  may  move beyond the site.
This type of failure could result  in the dispersion of
contaminants in the environment.

The  modeling approaches that would  be consistent
with simulating the effects that flow barriers would
have on the fate and  transport of radionuclides are
closely tied to the ability of the code to  accommodate
a number of factors,  including:   high permeability
contrasts, transient boundary conditions, and possibly
chemical   and  biological   reactions.     These
considerations will be discussed in greater detail in the
following sections.

The following are the types of physical,  chemical, and
biological processes that may need to be  modeled to
support alternative remedies based on isolation. Many
of these processes are very complex, and attempts at
modeling will meet with varying degrees of success:
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     !   Physical Properties and Processes
             unsaturated zone flow and transport
        •    runoff
             multiple layers
             vegetative cover
             transient source term
             extreme heterogeneity
             areal recharge and zero flux capability

     !   Chemical Properties and Processes
             localized ion exchange phenomena

     !   Biotic Properties and Processes
             localized biofixation
             microbial population modeling

Typical characterization data needs related to barrier
emplacement include:

     !   Barrier dimensions

     !   Barrier hydraulic conductivity

     !   Geochemical environment

     !   Structural integrity of barrie^arrier
        degradation

     !   Microbial environment

     !   Detailed hydrogeology
     !   Physical
             soil excavation (solid)
             pump and treat (vapor)
             in-situ vaporization (liquid)

     !   Biotic
             injection and removal of biomass foam

The following are the types of physical, chemical, and
biological processes that may need to be modeled to
support alternative remedies based on removal. Most
of these processes and properties are readily described
in mathematical terms and can be modeled relatively
reliably.  Obviously, modeling the biological activity
associated with the injection of a biomass will have the
same limitations that  are common to other types of
biological modeling.

     !   Physical Properties and Processes
             transient source term
             unsaturated zone flow and transport
             matrix diffusion
             desaturation and resaturation of the
             aquifer
             vapor transport

     !   Biotic Properties and Processes
             physical injection and withdrawal of the
             biomass
             microbial population modeling

Typical characterization needs related to radionuclide
removal include:
Removal

Radioactively contaminated soil can result from the
disposal of both solid and liquid waste.  Solid wastes
may have been buried in the  past without sufficient
integrity   of  containment   so  that,  eventually,
radioactivity intermingled with the  contiguous  soil.
Percolation of rain water through shallow burial  sites
can contribute further to the migration of radionuclides
to lower depths as well as to some lateral movement.
Wider areas of contamination  have occurred when
waste, stored temporarily at the surface,  has  lost
containment and has been disbursed by the wind.  The
technologies that  are most  commonly  applied  to
remove  solid,  liquid,  and  vapor  (e.g.,   tritium)
radionuclides include the following:
     !   Air permeability of the unsaturated zone
     !   Unsaturated zone flow and transport
        parameters
     !   Areal extent of contaminated wastes
     !   Depth to ground water
     !   Saturated zone flow and transport properties

The degree to which these factors are addressed in the
modeling relies heavily upon the objectives as well as
the availability of the required data.  Specific examples
of how these considerations are tied into the modeling
approach are provided in the sections that follow.

4.2.3.2  Transient Solutions

The  data that are available by the time the  remedial
design phase is entered usually span a relatively  long
time frame, which often allows the temporal nature of
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the hydrogeologic system to be relatively well defined.
If this is the case, the remedial design objectives could
involve many criteria that could not have been met
during  the   modeling  activities   in  the  site
characterization phase.   Many of these  additional
criteria of the design phase objectives may require that
the code have the capability to perform transient flow
and transport simulations.  This capacity would be
necessary to evaluate the effectiveness of a number of
remedial alternatives.  One such alterna-tive would be
the placement of earthen covers and a broad range of
natural and synthetic barriers, which are engineered to
establish a cap over surface and subsurface soil. One
of the objectives of the cover is to prevent rainwater
from  percolating  through contaminated soil and
carrying radionuclides to the ground water. In the site
characterization program, the objectives were such that
they  could probably  have been  met by assuming
constant areal recharge  over the  modeled area.
However, this steady-state approach would not account
for recharge  rates which vary through time, which
would be needed to simulate the deterioration of the
cap and the  subsequent effect on the radionuclide
leaching rates.

Soil excavation of radioactively contaminated soil will
result  in  some  amount  of residual radioactivity
remaining  in the soil  contiguous to the removal
operations. It could also result in the redistribution of
contaminants in the unsaturated zone. Without the
ability to  perform transient  simulations, with  the
source now largely removed, it would not be possible
to determine  how long it would take for the remedial
actions to have a noticeable effect on downgradient
receptors.

4.2.3.3  Multi-Dimensional

The  need to perform three-dimensional modeling
during the remedial phase will largely depend upon
what remedial alternatives are under consideration and
how the effectiveness of the selected alternative will be
evaluated.

The  remedial alternatives that are most commonly
supported by  three-dimensional  and  quasi-three-
dimensional modeling are those that  impart a strong
artificial stress to  the hydraulic  flow field,  such as
pumping wells and extraction trenches. Under many
circumstances,  the  vertical ground-water gradients,
prior to these imposed stresses, would be several orders
of magnitude less than the horizontal gradients and,
therefore, could  be  ignored in  a one-  or  two-
dimensional  flow analysis.   However, when the
hydraulic gradients  are  significantly  altered by
imposed  stresses,  three-dimensional   flow  fields
generally develop. Without the capability to simulate
the actual flow field in three dimensions, it would be
very difficult to effectively determine capture zones
and influent contaminant concentrations.   This is
largely because vertical leakance from units above and
below  the screened interval  of  the  extraction well
would  be ignored as  well as vertical concentration
gradients.

Another remedial alternative  that generally  creates
three-dimensional flow fields are physical barriers to
ground-water flow. Whether the barriers consist of
grout injection techniques, sheet pile cutoff walls, or
bentonite slurry walls, all of these  procedures will have
a common problem which is  that the hydraulic head
will build up behind the structures and induce vertical
gradients allowing ground water to  flow under the
barriers. In these cases, the analysis of vertical flow is
essential in determining probable  leakage rates and the
volume of water that would potentially flow through
the structure.

4.2.3.4   Transient Boundary  and  Non-Uniform
         Initial Conditions

Most of the  modeling analysis up until the  remedial
phase  can be performed with  constant  boundary
conditions.  This means that physical features within
the modeled area, such as the  water elevations of
surface water bodies  and areal recharge,  can be
simulated with values that remain constant with time.
Once the remedial phase is  reached, however, the
modeling objectives may require that the  transient
nature  of these boundaries are incorporated into the
analysis, and time-weighted averages may no longerbe
applicable.   For instance,  water bodies,  such as
radioactively contaminated  waste  lagoons,  would
probably have been treated as constant boundaries
during the site characterization  modeling, and their
water-surface  elevations  would  have  been  held
constant.  However, if one of the remedial activities
involved withdrawing contaminated water from one or
more of the lagoons, the effect that the change in
water-surface elevations would have on the  ground-
water gradients could be evaluated only by simulating
the drop in surface elevations through time.  This
would  be done by prescribing the boundaries of the
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lagoon(s) to change with time in order to simulate the
expected extraction rates.

The ability to prescribe boundaries within the model
would also be important in the evaluation of in-situ
soil flushing techniques, which are used to enhance the
mobility of contaminants migrating towards recovery
points. In this case, recharge would be varied through
time to reproduce the effects that various rates  of
flushing would have on  the ground-water flow and
contaminant transport.

Protective  barriers   to   ground-water  flow   are
constructed of very  low permeability  material and
emplaced either to prevent contaminated ground water
from migrating away from a site or to divert incoming
clean ground water from the source of contaminants.
If properly designed and emplaced, barriers to flow can
last  for  several  decades,  barring any geological
disturbances,  such  as   tremors,  ground  settling,
significant  changes   in  hydraulic  gradients,  etc.
However, if a barrier should fail following installation,
water  may  infiltrate the  site, and contaminated
leachates may move beyond the site. Therefore, the
effects that the failure of a barrier would have on
contaminant flow and transport should be evaluated
through modeling. There are a number of ways that
the failure of the barrier could be simulated. The most
straightforward method is to use transient boundaries
to simulate additional flow through the barrier as well
as a  reduction in the difference between water-level
elevations in front and behind the barrier. Therefore,
a code selected for this  simulation should  have  the
capability to incorporate transient boundaries.

4.2.3.5  Specialized Flow and Transport Processes

The  design and  evaluation of remedial alternatives
frequently  involve  the  consideration  of  flow  and
transport processes that were probably  not explicitly
modeled  during  the  site characterization program.
These  processes include:    complex   geochemical
reactions, matrix diffusion, heat flow,  and possibly
biological reactions.

As mentioned  previously,  numerical   models  that
satisfactorily  couple   ground-water  flow  and
contaminant  transport   to  complex  geochemical
reactions  simply  do  not  exist.    The  complex
geochemical  models  are based upon the laws  of
thermodynamics, which means  that  they predict
whether the potential exists for a particular reaction to
occur  within a  closed  system.    Despite  many
shortcomings  inherent  within the  methods  for
analyzing  complex geochemical   reactions,  it  is
important that the controlling geochemical reactions
be examined, possibly in laboratory benchscale or field
studies.    This  is  particularly  important  when
physical/chemical stabilization processes are  under
consideration whereby physical or chemical agents are
added to, and mixed with, a waste (typically sludge in
pits, ponds,  and lagoons),  with  the  objective  of
improving the handling or leaching characteristics of
the waste destined for land disposal.

A detailed understanding of the geochemistry can also
be very useful in estimating leach rates for uranium
mill tailings which otherwise would be associated with
possibly unacceptably high uncertainties.

Matrix diffusion is the process by which concentration
gradients cause contaminants either to move into or be
drawn out of low-permeability rocks where diffusion
governs contaminant transport rather than advection
and dispersion. Pump  and treat systems will tend to
draw water from the more permeable units, which may
leave large volumes of contaminants stored in the clays
and otherfine-grained materials, which will eventually
diffuse out.  Many computer codes do not adequately
simulate this very slow process. If matrix diffusion is
not accounted for, the contaminant movement will be
based solely upon ground-water velocities rather than
the  diffusion term.   Ground-water velocity will
generally move the contaminant much more rapidly
than diffusion, and clean-up times may be dramatically
underestimated.

In-situ  vitrification (ISV)  of  soils  is  a  thermal
treatment  and destruction  process that achieves
stabilization by  converting  contaminated soil and
wastes  into  chemically  inert, stable  glass and
crystalline products, resembling obsidian. Predicting
the effectiveness of IS V and its implementability would
require  a  number  of  specialized   processes  to be
modeled.  One such process would be vapor transport
of radionuclides, such as tritium, which would be an
important health consideration if the media were to be
heated.

A mechanism that appears to affect the transport of
radionuclides  under some conditions  is  microbial
fixation. Radionuclides may be immobilized and/or
mobilized by organisms or plants.  Immobilization
may occur if radionuclides are incorporated in the cell
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structure  of  microorganisms  or  plants  that  are
relatively stationary.  On the other hand, radionuclides
may be mobilized by forming biocolloids withbacteria,
spores, and viruses. Modeling of microbial processes
requires a code that, at  a bare  minimum, allows a
degradation rate to be assigned to the contaminant(s).

4.2.3.6  System Heterogeneity

The ability of a code to accommodate severe contrasts
in soil and rock properties is particularly important
during the design and evaluation of physical barriers
for protecting ground water.   If  the  application
involves  extending  the  barrier  down to  a  low
permeability strata to form a seal and deter underflow
leakage, it would be important that the code allow the
incorporation of multiple stratigraphic layers as well as
sharp hydraulic conductivity  contrasts.  Only in this
manner could the effect on contaminant flow  and
transport due to the effects  of leakage through the
barrier wall  and basement strata be evaluated.

4.3 SPECIFIC CONSIDERATIONS

The purpose of this section is to guide the Remediation
Manager and support personnel in determining what
specific capabilities are needed from a computer code
to address the modeling objectives.  The discussion
focuses on explanations  as to how specific  site  and
code  characteristics will provide the information
necessary to decide whether various code attributes
could  potentially  assist in the  analysis  or  be
detrimental to the analysis, or whether they are simply
unnecessary.

After the conceptual model  is  formulated  and the
modeling objectives are clearly defined in terms of the
available data, the investigator should have a relatively
good  idea  of the level of  sophistication that  the
anticipated modeling will require.  It now becomes
necessary to select one or more computer code(s)  that
have   the   attributes   necessary  to   describe
mathematically the conceptual model at the desired
level of detail. This step in the code selection process
requires detailed analysis of the conceptual model to
determine the degree to which specific waste and site
characteristics need to be explicitly modeled.

Fundamental questions that need to be answered at this
stage  in the code selection process are presented in
Table  4-2.    In  answering these  questions,  the
investigator must decide whether a particular code has
the required  capabilities  and  the  importance  of
individual  aspects of the conceptual model in the
modeling  analysis.     It  is  generally  relatively
straightforward to ascertain  whether a code  has a
specific capability, and many documents are already
available which provide this kind of information. It is
far more difficult to  decide whether or not a certain
attribute of a model is needed to accomplish  the
modeling objectives. Furthermore, other factors must
be considered in the code selection process which are
independent  of the  waste, site characteristics, and
modeling objectives. These factors are inherent in the
individual  computer codes  and  include:   solution
methodology, availability  of  the code, hardware
requirements, usability of the code, and the degree to
which the code has been tested and accepted.

Accordingly, this section has two goals:

1.  to  describe   the  detailed   waste  and   site
    characteristics and flow and transport processes
    that may need to be explicitly modeled in order to
    achieve the modeling objectives, and
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                      Table 4-2. Questions Pertinent to Model Selection
                          Site-Related Features of Flow and Transport Codes

Source Characteristics

    Does the contaminant enter the ground-water flow system at a point, or is it distributed along a line or
    over an area?

    Does the source consist of an initial pulse of contaminant, is it constant over time, or does it vary over
    time?

    Is the contaminant release solubility controlled?

Soil/Rock Characteristics

    Are anisotropy and heterogeneity important?

    Will fractures or macropores influence the flow and transport?

    Are discrete soil layers relevant to the analysis?

Aquifer System Characteristics

    What type of aquifers does the model need to simulate?  Confined, unconfined, or both?

    Does the model need to simulate complete dewatering of a confined aquifer?

    Does the model need to simulate aquitards?

    Does the model need to simulate the dewatering and resaturation of an aquifer?

    Do multiple aquifers need to be accounted for?

Transport and Fate Processes

    Which transport and fate processes need to be considered in the analysis (e.g., retardation, chain decay
    reactions, matrix diffusion)?

Multiphase Fluid Conditions

    Are all of the wastes miscible in water?

    Is the gas phase important to the analysis?

    Are density effects important?

Flow Conditions

    Will flow be under fully saturated or partially saturated conditions?	
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                                    Table 4-2. (Continued)
                        Code-Related Features of Flow and Transport Codes

Time Dependence

    Are the fluctuations in the hydrogeologic system significant, requiring transient analyses, or can they be
    ignored and simulated as steady state?

Solution Methodology

    How will the various mathematical methods used to solve the flow and transport equations affect the
    model results and therefore code selection?

    What will be the hardware requirements?

Code Geometry

    In how many dimensions is the code capable of modeling the  representative flow and transport processes?

Source Code Availability

    Is the code publicly available?

    If not, how much does it cost and is the source code available?

Code Testing

    Has the code been verified?

    Has the code been field-validated?

    Has the code been independently peer reviewed?

Code Input and Output

    What input data parameters are required?

    Does the code have a pre- or post-processor?

    Will the code provide breakthrough curves?

    How will the output depict plume extent?
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2.  to describe the  characteristics inherent in  a
    computer code that could influence the practical
    usefulness of the code, including the usability of
    the code and the extent to which the code has been
    tested.

Once these two objectives  are accomplished, the code
selection process becomes simply identifying the codes
that meet the modeling needs.

In light of these goals, this section is divided into two
parts, one addressing the  site-related characteristics
and the other addressing code-related characteristics
that must be considered when selecting a code.  Table
4-3   presents  a   matrix  relating  various  site
characteristics and an example of codes that explicitly
model those  characteristics.  Table 4-4  presents  a
matrix relating various code characteristics and an
example of codes that have those characteristics. The
following   sections  discuss  the  conditions  and
circumstances under which the various characteristics
are important.

Referring to Tables 4-3 and 4-4, it is not the intention
of this section to construct comprehensive reference
tables listing all available codes, but rather to provide
tables that clearly  illustrate the  criteria generally
considered in the identification of candidate computer
codes. Each of the criteria  is discussed individually in
context to its  relevance in answering the questions
identified in Table 4-2.

Once one or more computer code(s) are identified as
potential candidates, the codes should undergo further
review as a cross-check to ensure that the code has the
capabilities  that  are  specified  in the  literature.
Furthermore, a more  detailed  review can  provide
valuable insight into the nuances of the code which are
generally not available from cursory code reviews.

4.3.1   Site-Related Characteristics

The general components of the conceptual model that
need to be considered when selecting an appropriate
computer code are the following:

     !   Source Characteristics
     !   Aquifer and Soil/Rock Characteristics
     !   Transport and Fate Processes
     !   Fluid Conditions
     !   Flow Conditions
Each of these topics is presented as a major heading in
Table 4-3.  These broad subjects are further divided
into their individual components both in the table and
in the discussion that follows.

The objective of the subsequent presentation is not only
to discuss the relevance that each of the site- related
characteristics may have to the code selection process,
but also to provide criteria to determine whether a
particular attribute of a code will be important in the
analysis.

4.3.1.1  Source Characteristics

The accurate portrayal of the contaminant source term
is one of the most difficult tasks in the modeling
process.  All  too often there is a general lack of data
that  characterize  the  nature  and  extent  of  the
contamination as well as the release history. Computer
codes can accommodate the spatial distribution of the
contaminant  source  in several ways.   The most
common are the following:

     !   Point source
     !   Line source
     !   Area! source

Each of these source types can have an associated
release mechanism in which either the mass flux or
concentration is specified.  The two general types of
source-term  boundary  conditions   include   the
following:

     !   Concentration is prescribed
     !   Contaminant mass flux is prescribed

Source Delineation

The  determination of how  the spatial distribution of
the source term should be modeled (i.e., point, line, or
area) depends  on a number of factors, the most
important of which is the scale at which the site will be
investigated and modeled.  If the region of interest is
very large, when  compared with the contaminant
source area, even sizable lagoons or landfills could be
considered point sources.

Typically,  a  point   source  is  characterized  by
contaminants entering the ground water over a very
small area relative to the volume of the aquifer (e.g.,
injection well).  Line sources are generally  used
                                                   4-23

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      Table 4-3. Site-Related Features of Ground-Water Flow and Transport Codes
 Section 4.3.1.1   Source Characteristics
                    Point Source
                    Line Source
                    Areally Distributed Source
                    Multiple Sources
                    Specified Concentration
                    Specified Source Rate
	Time-Dependent Release	

 Section 4.3.1.2   Aquifer and Soil/Rock Characteristics
                    Confined Aquifers
                    Confining Unit(s)
                    Water-Table Aquifers
                    Convertible Aquifers
                    Multiple Aquifers
                    Homogeneous
                    Heterogeneous
                    Isotropic
                    Anisotropic
                    Fractures
                    Macropores
	Layered Soils	

 Section 4.3.1.3   Fate and Transport Processes
                    Dispersion
                    Advection
                    Matrix Diffusion
                    Density-Dependent Flow and Transport
                    Retardation
                    Non-linear Sorption
                    Chemical Reactions/Speciation
                    Single Species First Order Decay
	Multi-Species Transport with Chained Decay Reactions

 Section 4.3.1.4   Multiphase Fluid Conditions
                    Two-Phase Water/NAPL
                    Two-Phase Water/Air
	Three-Phase Water/NAPL/Air	

 Section 4.3.1.5   Flow Conditions
                    Fully Saturated
                    Convertible Aquifers
                    Variably Saturated/Non-Hysteretic
	Variably Saturated/Hysteretic	

 Section 4.3.1.6   Time Dependence
                    Steady-State
                    Transient
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     Table 4-4.  Code-Related Features of Ground-Water Flow and Transport Codes
 Section 4.3.2.1  Geometry
                    1-D Vertical/Horizontal
                    2-D Cross Sectional
                    2-D Area!
                    Quasi 3-D (Layered)
	Fully 3-D	

 Section 4.3.2.2  Source Code Availability
	Proprietary	

 Section 4.3.2.3  Code Testing and Processing
                    Verified
                    Field-Validated
                    PC-Version 3 86-SR486
	Pre and Post Processors	

 Section 4.3.2.3  Model Output
                    Contaminant Mass/Rate of Release to Ground Water
                    Contaminant Plume Extent
                    Contaminant Concentration as a Function of Distance
                    As a Function of Depth from Surface
                    Continuously Distributed in Space
                    Average at Selected Points or Cells
	Profiles at Selected Points Over Time	

 Appendix C  Solution Methodology
                Analytical
                    Approximate Analytical
                    Exact Analytical
                    Semi-Analytical
                Numerical
                    Spatial Discretization
                        Finite Difference
                        Integrated Finite-Difference
                        Finite Element
                        Method  of Characteristics
                    Temporal Discretization
                        Explicit
                        Implicit
                        Mixed Implicit-Explicit
                    Matrix Solvers
                        ADIP
                        Direct Solution
                        Iterative ADIP
                        SOR/LSOR/SSOR
                        SIP
                                               4-25

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when the contaminants are entering the aquifer over
areas where the length of the source greatly exceeds its
width, such as leaking pipes or unlined trenches.
Areal sources are often associated with agricultural
applications of fertilizers and pesticides. Uranium mill
tailings would also frequently be treated as an area!
source for modeling purposes.

In some instances, it  may  be desirable  to  model
multiple contaminant source areas.  This  would be
particularly important if cumulative health effects are
to be determined or if the extent  and nature (e.g.,
commingling  of  various  contaminant plumes) of
contamination will have a significant impact  on  the
remedial design.  It is possible, however, to perform
multiple-source modeling with codes  that do  not
inherently allow the incorporation of multiple sources.
The  most common approach to accomplishing this
objective is to perform a series of simulations in which
each model run assumes only one source. The  output
from each of the successive model runs is subsequently
cumulated into a  representative multiple-source site
model.

The number of dimensions (i.e., one, two, or three)
that will be explicitly  modeled will tend to impose
limitations on  how  a  contaminant source can be
modeled.

A point source can be  simulated with either a one-,
two-, or three-dimensional model, whereas a line or
areal  source must be modeled with either a two- or
three-dimensional model. One-dimensional codes are
constrained  to  simulating contaminant sources as
points.  The following four factors will  determine
whether the source should be modeled as a point, line,
or area source:

     !   Modeling objectives

     !   History of waste disposal activities

     !   Distribution of contaminants

     !   Fate and  transport processes

The modeling objectives are probably the single most
important factor in determining the way in which the
source term should be modeled.   One-dimensional
simulations  of point sources will yield  generally
conservative   approximations   of   contaminant
concentrations  because   of limited  dispersion.
Therefore, if the modeling objective is to determine
maximum  peak  concentrations   arriving   at
downgradient receptors, area and line sources could be
simulated as point sources comprised of average or
peak concentrations. However, if more realistic values
of concentrations and plume geometry are required, it
will generally be necessary to simulate the source term
characteristics more accurately.

Some knowledge of the history of the waste disposal
activities can often provide valuable insight into the
probable nature of the contaminant source term.  In
general, the  longer the site has been active, the more
likely it is that the wastes have been dispersed over a
larger area and discarded in many different forms.
The presence of product and waste lines immediately
suggests that line sources are present. Absorptionbeds
and  storage tanks indicate potential point sources,
whereas mill tailings, large lagoons, and air emissions
that carried and subsequently deposited contaminants
in the site vicinity would generally represent area
sources.

The distribution of measured contaminants in the soil
and ground  water will also provide clues as to  the
nature of their source. Contaminants that are wide-
spread and of  similar  concentrations suggest an area
source, while narrowly defined areas of contamina-tion
indicate a more localized or point source.

Dominating fate and transport processes should also be
considered when assigning source term characteristics.
If flow and transport properties are strongly confined
to one or two dimensions, as in the unsaturated zone
(i.e., liquids  flow down vertically due to gravity  in the
unsaturated  zone), it may  be possible to use a  more
simplified approximation of the source geometry (e.g.,
point).

Release Mechanism

Computer codes  can  simulate  the introduction  of
contaminants to the ground water as an instantaneous
pulse or as a continuous release over time.   A
continuous release may either be constant or vary with
time.  The two most  common means of simulating
continuous or  pulse releases are by either specifying
release   concentrations   or   by  specifying   the
contaminant mass entering the  system.  In general,
both approaches have  drawbacks and limitations and
require considerable thought and possibly a number of
independent  calculations prior  to  selecting  and
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implementing the  most appropriate method for the
modeling exercise.  Furthermore, most ground-water
flow and transport codes do not explicitly account for
the physical degradation of waste containers  and,
therefore, anticipated release rates must be estimated
through other means (e.g., waste package codes) and
input as boundary  conditions into  the  flow  and
transport model.

It  is generally preferable to  pose the  source-term
release in terms of contaminant mass flux, rather than
specified concentrations.  This is true  even if the
concentration at the source is known.  The primary
problem  with specifying the concentration  of the
contaminants entering the system is that care must be
taken to  ensure that the total mass that enters the
system does not exceed that which would actually be
available from the source.  Furthermore, specified
concentrations  tend  to  over-predict contaminant
concentrations near the source because the effects of
dilution and dispersion are not properly accounted for.
However,  it  is  not  uncommon   for  specified
concentrations  to  be used if the release of the
contaminant is controlled by its solubility limit; that is,
if  the  contaminant is  relatively  insoluble.   The
rationale  for  this   approach  is that  specified
concentrations would tend to describe leaching  rates
that are solubility controlled.

Not all computer codes  allow the concentration or
mass of a continuous release to change with time.  This
quality is particularly important if it is suspected that
conditions in the past or future are not approximated
by those of the present. A specific example would be
modeling the performance of an  engineered barrier
whose performance is expected to change with time.

Radioactive source terms present special considera-
tions in that the mass fraction of the parent isotopes
will  diminish with time due  to radioactive  decay.
However, if the radionuclide mass release is solubility
controlled,  the concentration of  the  leachate  may
remain constant despite the decay of the source term.
The release concentrations may remain constant until
the source term has decayed to concentrations where
solubility limits no longer dictate the  amount of
radionuclides that may go into the solution.
Computer codes have been developed that can simulate
single  or multiple  aquifers which may  behave  as
confined, unconfined, or change from one condition to
another.  Intrinsic characteristics of the aquifers and
aquitards, which control flow and transport, are also
simulated to various degrees by computer codes. The
most common code selection criteria with regard to
aquifers and their characteristics include the following:

    !    Confined aquifers

    !    Water-table (unconfined) aquifers

    !    Multiple aquifers/aquitards

    !    Heterogeneous

    !    Anisotropic

    !    Fractures/macropores

    !    Layered soils/rocks

Water-Table and Confined Aquifers

The ground water flowing within a water-table aquifer
is in immediate contact with the atmosphere and is
directly recharged through the overlying unsaturated
zone.  This water-table surface is equal to atmospheric
pressure  and is free to rise and fall within the aquifer
in response to varying amounts of recharge (e.g., rain).
The water-table aquifer generally follows land-surface
topography and is frequently revealed in the form of
surface-water bodies such as lakes and rivers (Figure
4-6).

A confined aquifer is one in which the ground water is
isolated from the atmosphere by some geologic feature
(e.g., confining unit). As a result, the ground water is
under pressure greater than that of atmospheric, and,
if a well penetrates a confined aquifer, the water in the
well will rise above the top of the aquifer.

In most  circumstances,  the water first encountered
beneath the site will be under water-table  conditions.
However, this does not always mean that water levels
measured in wells  are indicative of the water-table
4.3.1.2  Aquifer and Soil/Rock Characteristics
                                                   4-27

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                  \      r   x/
Figure 4-6.   Water Table and Confined Aquifers
surface.  This discrepancy may occur when a well is
screened below the water table in an  unconfined
aquifer with large vertical gradients (or a well with a
very long screen in an unconfined aquifer with large
vertical gradients).  In many instances, particularly
with domestic wells, water in the shallow water-table
aquifer has been cased off and a deeper unit, that may
be under confined conditions, is supplying water to the
well.  The importance of this is that the water in a well
that taps a confined  aquifer can rise significantly
higher in the well than the true water-table surface. If
this is the case, the thickness of the unsaturated zone
may be significantly underestimated.

The mathematical descriptionforground-waterflow in
a water-table aquifer is more complex than that for
flow in a confined aquifer. This is largely because the
saturated thickness of a water-table aquifer will vary
with time and, therefore,  the transmissivity (which is
the quantity of volume of water flowing through the
aquifer, mathematically calculated as the product of
the hydraulic conductivity and the vertical thickness of
the aquifer) is also time dependent. Confined aquifers
always   remain   saturated  and,   therefore,   the
mathematics  do not have to account for a varying
transmissivity.

Computer codes that simulate confined aquifers can
also be used to simulate water-table conditions if the
saturated thickness of the aquifer is not expected to
vary by more than ten percent over the time of interest.
This assumption would generally be appropriate if the
modeling objectives can be met by assuming steady-
state conditions.  If significant changes (greater than
ten percent) in the water-table elevation are expected
over the time of interest, not only would a steady-state
modeling approach be of uncertain value, but the
validity of  applying  a computer code designed to
simulate  confined flow to  problems that involve
unconfined flow would be questionable.

The importance of whether the system is under steady
state or transient conditions dictates that the length of
the time of interest needs to be carefully considered in
context of the code  applicability.   In general, the
shorter the time of interest the  more likely it is that
fluctuations of the water table will exceed ten percent
of the saturated thickness.  As the length of the time of
interest increases, long-term averages tend to dampen
out the extremes within the water-table fluctuations.

Examples of conditions where a code developed for
confined conditions would probably not be applicable
to simulate ground-water flow in water-table aquifers
include:

     !   Highly variable recharge rates

     !   Ephemeral effects of surface-water bodies

     !   Remediation activities
!
        Physical properties of the contaminants
Shallow ground-water flow systems that are recharged
primarily from percolating precipitation tend to be
strongly influenced by  seasonal fluctuations of the
local climate.  Summer droughts and  spring snow
melts can cause  dramatic shifts in the water-table
elevation. For reliable seasonal predictions, computer
codes would have to be able to simulate changes in the
aquifer transmissivity through time.  Such is not the
case if the use of long-term recharge averages could be
justified, as when estimating average annual radiation
doses associated with the drinking water pathway.

In many cases, water-table aquifers are closely tied to
surface-water bodies which are ephemeral in nature.
These surface-water bodies may include intermittent
and ephemeral  streams,  waste lagoons, and  tidal
marshes.  It is important that the transient effect of
these features  on the water table be considered when
selecting an appropriate computer code.
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Remediation  activities   may   also   create   large
oscillations of the water table.  Activities that include
active remediation, such as pump and treat, artificial
recharge,  and ground-water injection will generally
have the greatest impact on the ground-water table.
Relatively passive remediation activities,  such as
ceasing the disposal of liquids into lagoons or streams,
may also  affect the  shallow aquifer by causing the
water table to find a new  equilibrium which may or
may not be  significantly  different from  the  initial
position.

A special consideration  for  modeling water-table
aquifers,  particularly  when  the  aquifer  is  being
significantly  dewatered,  as  in  pump  and  treat
operations, is that not all computer codes with the
capability to simulate water-table aquifers have the
capacity  to  resaturate  the  aquifer if it becomes
completely dewatered.  This  could pose a serious
limitation if one of the objectives is to evaluate the
effectiveness of a pump  and  treat system that is
operated intermittently.

In determining whether a computer code that does not
simulate water-table conditions is appropriate,  some
consideration needs to be given to the nature  of the
contaminants.  For  example,  the flow of  LNAPL
(contaminants less dense than water, such as  oil) is
complicated  by  the rise and fall of the water table
within the seasons. As the water table falls, the layer
of mobile contaminant also falls. When the watertable
rises, the contaminant also rises.  However, residual
contamination is left behind in the saturated zone. If
the water  table rises faster than the contaminant can
rise, "pockets" of free contaminants might become left
below  the water  table.  The flow  of water and
contaminants is controlled by Darcy's law and depends
upon the  effects of density,  viscosity, and relative
permeability. Depending upon these factors, either the
contaminant or the water could have a greater velocity
as the water table rises and falls.  Therefore, in order
to predict remediation times accurately, the volume of
the contaminant remaining in the unsaturated zone
needs to be estimated.  If the code does not allow the
water  table   to  rise  freely within the aquifer, the
interaction between  the contaminant and the  water
table cannot be simulated.

Relatively few computer codes have been developed
that will simulate conditions within an aquifer that are
changing  from  confined  conditions  to water-table
conditions.  This capability is  particularly useful for
simulating a ground-water system where a confined
aquifer will be  heavily  pumped and potentially
dewatered.

Multiple Aquifers/Aquitards

Computer codes have been developed that can simulate
either single or multiple hydrogeologic layers (Figure
4-6). Generally, a single-layer code is used if the bulk
of the contamination is confined to that layer or if the
difference  of the flow and transport parameters
between the various layers is not significant enough to
warrant the incorporation of various layers.

In deciding whether there is a significant difference in
the  flow  and transport  properties between various
layers, the investigator should keep in mind that the
parameter values that could vary  from layer to layer
include:   hydraulic conductivity, effective porosity,
distribution coefficients,  and bulk densities.  In most
instances, effective porosities, distribution coefficients,
and bulk densities are estimated from the literature and
could  have  a  large  associated  error.    Hydraulic
conductivities,  which are typically measured  in the
field, also may be off by an  order  of magnitude.
Therefore, it generally does not make much sense to
model  discrete  layers if estimated parameter values,
separating different layers, fall within probable error
ranges.     Furthermore,  unless   the  discrete
hydrogeologic units are continuous over the majority
of the  flow path,  it  is often possible to model the
system as one layer using average flow and transport
properties.

The greater the  depth to which the system is modeled,
the  more likely it will be that aquifers of varying
characteristics will be encountered. Ideally, the depth
to which the system should be modeled is the depth at
which  ground-water  gradients  become consistently
vertically upward. This depth will define the basement
flow of the shallow system, and most contamination
would   be  confined  to  shallower  depths   unless
contaminants are being driven downward against the
ambient ground-water flow by density gradients.

If very little information is available on the distribution
of vertical gradients, a general rule that is often useful
in estimating the relative base of the flow system is
that discharge areas (e.g., perennial streams, lakes, and
swamps) are  associated with upward gradients, while
recharge areas (e.g.,  mountains  and uplands)  are
typified by downward gradients.  Thus, it is more
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likely that the vertical extent  of contamination is
greater when the contaminant source is located in a
recharge area than in a discharge area.

Layered Soils/Rocks in the Vadose Zone

Rarely would soils and rocks within the vadose zone
not exhibit some form of natural layering.  The first
consideration as to how this natural layering should be
treated in the modeling analysis is related to whether
the various soil layers have significantly different flow
and transport properties.  If these properties do not
vary from layer to layer, then there would be little need
for the code to have multiple-layer capability. On the
other hand, if the layers have distinctive properties that
would affect flow and transport, a decision needs to be
made how best to achieve the modeling objectives; i.e.,
should each layer be discretely treated or should all of
the layers be combined into a single layer?

In most instances, it would be appropriate to combine
the layers  into a single layer for all phases  of the
remedial  program  with  the   following  notable
exceptions:

    !   Vapor-phase transport

    !   Model calibration
     i
        Conceptual model development
Vapor-phase transport within the vadose zone, which
can occur with tritiated water vapor, will be largely
controlled by the various flow properties of the soils
within the unsaturated zone.  Vapors  will tend to
congregate beneath layers with low air permeabilities
and freely move through more permeable layers. The
direction of movement of the vapor is often governed
by the dip and orientation of the soil beds above the
water table and are independent of the ground-water
gradients.

Percolating   rainwater  may   induce   a  phase-
transformation of radionuclide vapor back to a liquid
phase, thus allowing transport to the saturated zone.
If this  process  occurs  in  beds  through  which
radionuclide vapors have migrated, both away from the
source and up the ground-water gradient, it is possible
that  significant amounts of radioactivity  may be
detected in the ground-water upgradient of the source
area.
This phenomenon is particularly important to consider
when determining how far upgradient background
monitoring wells should be placed to ensure that the
ambient ground water has not been contaminated via
vapor transport from the contaminant source. In many
systems, with relatively thin vadose zones (< 10 m), it
may be  more practical  to  approach this  problem
empirically and  simply measure radionuclide vapor
concentrations in the unsaturated zone. However, the
expense of investigating relatively thick vadose zones
(> 50 m) is often significant, and modeling could be
very useful in estimating the likely distance that vapor
may have moved.

An evaluation of expected vapor movement  and
concentrations could also be of considerable value
depending upon remedial measure alternatives.  For
instance, it may  be desirable to predict the  potential
movement of vapor out from under a remedial cap or
the movement of water vapor under a capped area.
Without  the  ability  of the code  to  accommodate
discrete layers, the effect  that a low permeability cap
would have on vapor transport could not be simulated.
Under  other  circumstances, maintenance- related
issues could be  addressed,  such as the build- up of
hydrogen gas within landfills that contain pyrophoric
uranium (i.e., spontaneously combustible). In landfills
where pyrophoric forms of uranium metal were placed
in  drums and  submerged  in  petroleum-based  or
synthetic oils to  prevent rapid oxidation, there is the
potential for the uranium and petroleum to  react to
form   hydrogen  gas   which,  at  high   enough
concentrations, is an explosion hazard.

Models are generally calibrated against measured field
values.  However, unless the field characteri-zation
program was designed to characterize the unsaturated
zone,  data are frequently insufficient to calibrate a
vadose zone model. Soil sampling would have had to
provide vertical, and in many instances horizontal,
profiles   of  radionuclide  concentrations,   soil
permeability, and moisture content data. Therefore, it
is important to decide prior to site characterization
whether a fully calibrated vadose zone transport model
will be required to meet the modeling objectives. After
the characterization is completed, itcanbe determined,
from the data, whether a code is needed that will allow
the simulation of discrete  layers.

Calibration  of  flow  and  transport  through   the
unsaturated zone generally becomes important in areas
with relatively thick unsaturated zones (> 100 m).  In
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these areas, deep boreholes are both very expensive to
install and  difficult  to  instrument.   Under these
circumstances, a calibrated model may be useful in
performing mass-balance calculations to determine the
depth  that  contaminants  could  have  potentially
migrated, and to provide an estimate of contaminant
volumes requiring remediation.

An accurate portrayal of the site-conceptual model is
essential for all phases of the remedial program.  A
computer code with the capability to allow layering
may facilitate the evaluation of various  aspects of the
conceptual model.  For example, infiltration through
the vadose zone may  move laterally over significant
distances, particularly when there are soil layers of low
permeability which impede vertical migration and
allow saturated flow to occur in perched-water zones
(Figure 4-7).  This transport process is particularly
important in areas where a relatively thick unsaturated
zone is bisected by deep-cut streams, and the perched
water  movement  in  the  unsaturated   zone  is
predominantly   horizontal   rather  than  vertical
infiltration  to   the   water  table.     Under  these
circumstances, the radionuclides may short-circuit the
ground-water pathway and discharge  to seeps and
springs along the river wall.  Therefore, it could be
important to evaluate the potential for horizontal
movement in the unsaturated zone to ensure that all
exposure pathways are properly accounted for in the
conceptual model.

Anisotropic/Isotropic

In a porous medium  made of  spheres of the same
diameter packed uniformly, the geometry of the voids
is  the  same in all directions.   Thus,  the intrinsic
permeability of the unit is the same in all directions,
and the unit is said to be isotropic. On the other hand,
if the geometry of the voids is not uniform, and  the
physical properties of the medium are
                       ""d;..
        S....I
Figure 4-7.   Perched Water
dependent on direction, the medium  is said to be
anisotropic.

Anisotropy can play a major role in the movement of
ground water and contaminants. In most sedimentary
environments,  clays  and  silts  are  deposited  as
horizontal layers.  This preferential orientation of the
mineral  particles  allows the horizontal hydraulic
conductivities to greatly exceed those in the vertical
direction.   As  a  general  rule,  for  sedimentary
environments, it is assumed that horizontal hydraulic
conductivities are 10 to 100 times greater than those in
the vertical direction.

If  the  modeling  analysis  does  not account for
anisotropy, the contaminants will be predicted to be
more dispersed in the  vertical direction  than would
probably be occurring  in the real world.  One of the
primary  drawbacks  to this  taking place is that the
predicted  concentrations  would  be  significantly
reduced due to this  artificial vertical dispersion and
resulting dilution.

Macropores/Fractures

Modeling flow through the unsaturated zone is based
on the assumption that  the  soil  is  a  continuous
unsaturated solid matrix that holds water within the
pores. Actual soil, however, has a number of cracks,
root holes, animal burrows, etc., where the physical
properties differ enormously from the surrounding soil
matrix (Figure 4-8).  Under appropriate conditions,
these  flow  channels  have  the  capacity  to carry
immense amounts of water  at velocities  that  greatly
exceed those in the surrounding matrix.
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Figure 4-8.   Macropores and Fractures
At present, there is no complete theory describing
water  flow  through  these  structural  voids  or
macropores.   There  is  uncertainty  regarding the
significance of subsurface voids in water flow, since, if
large, they should fill only when the surrounding soil
matrix is close to saturation. Nonetheless, studies have
shown that contaminants can  migrate to substantial
depths with only a small amount of water input.

Many water flow processes of interest, such as ground-
water recharge, are  concerned only  with  areally
averaged water input. Therefore, preferential flow of
water through structural  voids does not necessarily
invalidate the code formulations that assume uniform
flow and do not directly account for
macropores. However, preferential flow is of critical
importance in solute transport because it  enhances
contaminant mobility and can significantly increase
pollution hazards.

Since codes do not exist that  directly simulate flow
through macropores, it is important to select a code
with features that will allow an indirect simulation of
the effects of macropores on flow and transport. A
number  of factors should   be considered  when
determining whether macropores are important in the
modeling  analysis, including:
     !   Presence, geometry, and spatial distribution
        of macropores
     !   Location of the waste relative to
        macropores
     !   Rainfall duration, intensity, and runoff

Determining the presence of macropores may sound
relatively straightforward; however, in many instances,
the formation of macropores is an ephemeral process
where the desiccation and shrinkage of clays will occur
only during the summer months or after long periods
of drought. Therefore, if it is suspected that conditions
are suitable for the formation of macropores, a special
effort should be made to  tour  the site  during the
periods when macropores are most likely to be present.
After establishing the  existence of macropores, the
next step would be to gain some understanding of their
geometry and spatial distribution. If macropores are
relatively  shallow (< 1 m), it is  highly unlikely that
they would have a significant effect on the flow and
transport even if they are closely  spaced. However, if
the macropores are relatively deep compared to the
thickness of the unsaturated zone, on the order of ten
percent, their effect on flow and transport should be
considered in the modeling exercise.
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The location of the wastes relative to any macropores
plays  a  significant  role  in  determining   their
importance.  Obviously, if the contaminated area is
dissected by numerous relatively  deep macropores
extending  well  below  the  wastes,  it  would  raise
concerns that flow and radionuclide transport may be
facilitated due to their presence. On the other hand, if
the wastes are buried below the maximum depth of the
macropores, or if the site has been capped or covered
with  a material that is  not  prone  to macropore
development, their presence  would play a lesser role.
The direct effect that the macropores will have on the
mobility of the wastes is closely tied to whether the
macropores are located beneath the waste.  If so, they
may be providing an avenue for radionuclide transport
or, if they  terminate  above  the waste, they may be
indirectly enhancing  transport by allowing greater
amounts of recharge to come in contact with the
contaminants.

The rainfall duration, intensity, and runoff also play a
major role  in evaluating the relative  importance of
macropores on radionuclide transport.   If an area is
prone   to   high-intensity,  short-duration  storms
(convective precipitation) with low runoff, the rainfall
rates may exceed matrix infiltration rates, and it is not
necessary for the soil to become saturated before water
can flow within the macropores. In this manner, water
and/or contaminants can move well in advance  of the
wetting front and  be carried beyond  the  maximum
saturation extent of the soil matrix. In contrast, in an
area  which is  typically  subjected to  long-duration
rainfall events with low intensities, it is more  likely
that flow will not occur in the macropores but will be
confined to the soil matrix.  This is because the soil
matrix infiltration  rate will  exceed the rainfall rates
characteristic of this cyclonic precipitation.

As mentioned  previously, there are  no codes  that
directly  simulate  flow  and  transport   through
macropores in the unsaturated zone. Therefore, if it is
determined that macropores  are present and may
potentially  have an important effect  on flow  and
transport, several approaches could be used to account
indirectly  for the  flow  and  transport within the
macropores.  These approaches  are based upon the
geometry of the macropores, location of the wastes,
and rainfall characteristics.  Each of the approaches
will  require  a  code with the proper  attributes, as
outlined below.
If the maximum depth of the macropores is above the
top of the wastes  and rainfall occurs at such an
intensity  that  flow  will  take  place within  the
macropores, it will be necessary to evaluate the effect
that additional water reaching the wastes will have on
contaminant   transport.     To   account   for   this
phenomenon, the code will need the ability  to regulate
recharge as well as infiltration rates.  More precisely,
the code must be very stable numerically and able to
accommodate areally variable and transient recharge,
anisotropy, and heterogeneity.  In  essence,  higher
recharge rates are applied over short time intervals to
areas of the site with known macropores. However, in
order to enable the soil to absorb the  additional water
and to simulate greater infiltration rates,  the soil in
this area must also  be assigned larger hydraulic
conductivities with high vertical to horizontal ratios.
To handle these sharp soil material contrasts, the code
must be well formulated and not be  plagued with
convergence problems (see Appendix C).

In instances where macropores extend beneath the
bottom of the buried wastes, several alternatives exist
for modeling  their potential effect on  flow  and
transport. The most  straightforward approach is to
simulate the portion of the macropores that extend
below the wastes by removing an equivalent thickness
from the modeled unsaturated zone.  This  essentially
assumes  instantaneous  transport  through  the
macropores  and would result in very  conservative
values. This approach has a number of advantages, the
greatest of which is that the computer code does not
need any additional  features than  it  would have
otherwise needed without the macropores.  However,
if this approach is thought to be overly conservative,
which would probably be the case if more than half the
thickness of the unsaturated zone would need to be
removed, an alternative  could be employed which
involves methods  that  are  used to simulate deep
fractured networks in the vadose zone.

Determining  the importance  of fractures  within the
unsaturated zone generally presents more of a problem
than making the same determination for macropores
because: (1) fractures are usually not  visible from the
surface   and  are  difficult  to  characterize  in  the
subsurface; (2) if fractures are present, they will often
extend through the  entire unsaturated zone and into
the saturated zone; and (3) fractures may serve as
either conduits or barriers to flow. All of these issues
must be addressed in the site characterization program
to  determine   whether the  fractures   need  to  be
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considered in the modeling.  In general, fractures that
can be traced through the waste area are important and
should be considered, at least conceptually, in the
analysis.

Fracture modeling  of the  unsaturated  zone  can
generally  use computer codes with  attributes very
similar to those used for modeling macropores with a
few  notable exceptions.  For the purposes  of this
discussion, it is assumed that the fractures are found to
extend through the unsaturated zone into the saturated
zone, and that an assumption of instantaneous flow
through the entire vadose zone thickness would not be
acceptable for the analysis. Unlike macropores, which
will  probably not extend to  depths  greater than 5
meters,  fractures may reach depths on the order of
hundreds of meters.   This  factor has a number of
implications for both the flow of water and transport of
radionuclides.

Rainfall percolating through a fracture will slowly
diffuse into the soil matrix. Thus, eventually the water
moving in the fracture will  become so  depleted that
fracture flow will  no longer develop  unless other
sources  of water are intercepted (e.g.,  perched).  The
depth at which fracture flow would cease depends on
a number of factors including fracture properties,
rainfall characteristics, and soil matrix qualities, all of
which are  closely  interrelated and are difficult to
quantify. Conceptually, this process of diffusion into
the matrix  at  depth suggests a  direct correlation
between the importance of the fractures and the depth
of the unsaturated  zone.  That is, at  some depth,
fracture flow will no longer be important.

There will always be  a large degree  of subjectivity
associated with deciding the importance of fractures'
effects on flow and  transport within the vadose zone.
However, it would probably  be safe to assume that in
most unsaturated systems, fracture flow below  200
meters is insignificant unless a continuous  source of
water is available (e.g., overlying adsorption beds).

The  features  of computer codes that would be
necessary to describe fracture flow would be similar to
those required to simulate  macropores, except  that
now, because the pulse-like nature of  the recharge
would be dampened  at  greater  depths,  it would
probably not be necessary for the code to accommodate
transient recharge, particularly if the depths of interest
are greater than 50 meters.  However,  the codes must
still be very stable numerically and able to incorporate
anisotropy and heterogeneity, which are discussed in
greater detail in the following sections.

Almost all of the discussion to this point has focused
upon modeling flow and transport in porous media. It
is  important to  realize, however,  that a number of
radioactively  contaminated sites overlie areas where
fractures and solution channels are probably dominant
mechanisms for flow and transport. The uncertainty
associated with  fracture zone modeling is generally
high, and if fracture modeling is to be successful, a
concentrated effort needs to go into the design of the
field investigation. Therefore, the benefits associated
with modeling fractured flow and transport processes
have to be carefully weighed against a number of
deterrents which include:

     !   An expanded field program is needed;
     !   Significant uncertainties are associated with
        fracture characterization methods;
     !   High degree of expertise  is required of the
        modeler;
     !   Codes available to simulate fracture flow are
        difficult to use.

A  number of analytical models are available  that do
simulate ground-water flow and radionuclide transport
through fractures.   However,  it  is unlikely  that
analytical models could adequately describe flow and
transport processes in most fractured systems because
these processes are much more complex than those in
unfractured granular porous media.  This is due to the
extreme heterogeneities, as well as anisotropies, in the
fractured systems.  When a radionuclide is introduced
into  a fractured  porous medium, it migrates through
the fracture openings by means of advection as well as
hydrodynamic dispersion.   The  radionuclide  also
diffuses slowly  into the porous matrix.   Molecular
diffusion dominates flow  and  transport within the
porous matrix because the fluid velocity in the porous
matrix is usually very small. Upon  introduction of the
radionuclide into a fractured aquifer, the  radionuclide
moves rapidly within the fracture network. As time
progresses, the  zone of contamination  will  diffuse
farther into the porous  matrix.   Since the  porous
matrix  has a  very large capacity to  store  the
contaminant, it plays a significant role in retarding the
advance of the concentration front in the fractures.  If
the source of contamination is discontinued and the
aquifer is flushed by fresh water, the contaminant mass
in the fractures  will be removed relatively quickly,
whereas the contamin-ant in the porous matrix will be
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removed very slowly via diffusion back to the fracture
openings.

In general,  data  limitations and narrow objectives
would preclude the modeling of fractured systems until
at least the Site Characterization  phase.   If it is
determined that numerical modeling of a fractured
system   will   be  performed  during  the  Site
Characterization, it becomes necessary to evaluate the
data needed to support fracture flow and transport
numerical  modeling.    In  order  to  adequately
understand the potential data requirements for fracture
flow  and transport  modeling,  the  following text
provides a very  basic  understanding of modeling
fractured systems.

At present there are two general numerical methods for
solving  flow and transport in a fractured medium:
modeling of the flow, accounting for the fractures one
by one,  or modeling with an equivalent continuous
medium approach.

Flow and transport modeling in a fracture system by a
continuous porous medium approach is performed by
assigning each family  of  fractures a directional
conductivity, thus constituting a hydraulic conductivity
tensor.   As the  frequency  and direction  of these
conductivities  are defined,  the principal  axes  of
anisotropy of the tensor and the conductivities in these
directions can be calculated.  It is thus assumed that
the fracture spacings are frequent enough that, when
viewed  from the perspective of the entire physical
system,  flow  and  transport  processes would  be
consistent with those associated with porous media.
Therefore, computer codes developed for porous media
may sometimes be used to simulate multiple fracture
families.  This approach relies heavily  upon  the
presence of multiple fractures. However, if there are a
relatively limited number of fractures, as is often the
case with solution channel(s) or faults, an alternative
approach is necessary.  This alternative approach
consists of three general methods, which are termed
dual-porosity, dual-permeability, and discrete fracture.
All of these methods need a computer code that is
specifically developed for modeling fracture flow. The
code will have separate equations which are developed
for flow and transport in the rock  matrix  and  are
coupled to equations describing flow and transport in
the fractures. This allows fractures to be assigned flow
and transport properties which are discrete from the
matrix properties. The dual-porosity method assumes
that fractures are relatively uniformly spaced and does
not  allow  flow  to occur  among  matrix blocks.
Contaminants leave and enter the fractures  only
through diffusion.  The dual-permeability  approach
also assumes that fracture networks are well developed
although this method  does  allow advective and
dispersive flow  through the matrix blocks  and is
conducive to simulating highly fractured systems in
which both the matrix and the fractures are relatively
permeable. The discrete fracture approach is similar
to the dual-permeability method although the discrete
fracture method allows single fractures to be modeled
separately as  line elements.

In most instances, it is very difficult to obtain the field
data necessary to perform detailed fracture  flow and
transport modeling.  Such modeling could  require a
substantial   dedication  of  resources,  and  any
commitment  should be carefully weighed against that
which  may  be   gained  from  the  modeling.
Circumstances that could lead to a decision to perform
fracture-flow modeling may include:

     !   Future risks  cannot  be  assessed without
        explicitly accounting for flow and transport in
        a fractured system;
     !   Sensitivity or bounding analyses cannot  be
        designed to meet objectives; and
     !   Empirical data are either not available or can
        not  be  effectively  used to estimate  risks,
        capture zones, influent concentrations, etc.

Homogeneous/Heterogeneous

A homogeneous unit is one that has the  same
properties at all locations. For a sandstone, this would
indicate that the  grain-size distribution,  porosity,
degree of cementation, and thickness are variable only
within small  limits. The values of the transmissivity
and storativity of the unit would be about the same at
all locations.  A plutonic or metamorphic rock would
have  the  same  amount of fracturing  everywhere,
including  the strike and  dip  of the joint  sets.  A
limestone would have the same amount of jointing and
solution openings at all locations.

In heterogeneous  formations,  hydraulic properties
change spatially.  One example would be a change in
thickness.  A sandstone that thickens as a  wedge is
nonhomogeneous,   even   if   porosity,  hydraulic
conductivity, and specific storage remain constant.
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Most numerical computer codes have the ability to
assign varying hydraulic conductivities and storage
properties  to  the  hydrostratigraphic  units  being
simulated.  Furthermore, computer codes have also
been  developed that have  the  ability  to simulate
constant or variable thicknesses.

Analytical  methods are  constrained  to  modeling
aquifers that do not change significantly in thickness
or other aquifer characteristics. Numerical codes may
or  may  not  have been developed  for problems
involving an aquifer of variable thickness. Numerical
codes that do not allow the thickness of the aquifer to
vary significantly use transmissivity as the model input
parameter which indirectly describes aquifer thickness
(hydraulic  conductivity  multiplied by  thickness).
However, numerical  codes that specify  hydraulic
conductivity and aquifer thickness as input parameters
independently   calculate   aquifer  transmissivity
throughout the model domain and, therefore,  allow
aquifer thickness to vary.  If advective-dispersive
contaminant transport calculations are expected to be
performed at some time in the analysis, it is important
that hydraulic conductivities and aquifer thicknesses
are  known  even  when  their  product  (i.e.,
transmissivity) is only required as model input. This
is because the quantity of ground-water flow through
aquifers of identical transmissivity will be the same
under equal gradients. Therefore, an aquifer which is
very thick and  has a low hydraulic conductivity  can
have an identical transmissivity to that of another
aquifer which is  thin  but has  a high  hydraulic
conductivity.   As  far  as  the  bulk movement of
groundwater is concerned, the two systems will behave
in a  similar fashion when comparative  boundary
conditions  are  applied.   However, the transport of
radionuclides would behave very differently within the
two systems, in that velocities would generally be
much  greater  in  systems  with  higher  hydraulic
conductivities.

A  few finite-element computer codes use what are
termed curvilinear elements. These are specialized
elements that can be spatially deformed to  mimic the
elevations of the upper and lower surfaces of the
hydrogeologic  units.    Curvilinear  elements  are
particularly useful when aquifers and aquitards have
highly variable thicknesses.

In general, if it is expected that the aquifer thickness
will vary by more than ten percent, it is recom-mended
that the computer  code be capable  of simulating
variable thicknesses.   If a code  does not properly
simulate the aquifer thicknesses, the contaminant
velocities  will be  too large in  areas  where  the
simulated aquifer is  thinner than the true aquifer
thickness and too small in those regions that have too
great a simulated thickness.

The ability to simulate aquifer heterogeneities may also
be very important during the remedial design phase of
the  investigation.  If engineered barriers  of low
permeability  are evaluated  as  potential  remedial
options, it would be necessary to determine their
overall effectiveness.   In this scenario, it would be
important not only to select a computer code that can
simulate highly variable hydraulic conductivities, but
also  to ensure that the sharp contrasts in hydraulic
conductivities   do  not  cause  instabilities  in  the
mathematical solutions.

4.3.1.3  Transport and Fate Processes

The transport of radionuclides by flow through either
a porous matrix or a fractured system will, in each
case,  be  affected by various  geochemical   and
mechanical processes. Among the chemical processes
are adsorption on mineral surfaces (both internal  and
external to the crystal structure), including the kinetics
of adsorption, and processes leading to precipitation.
The  mechanical processes are advection,  dispersive
effects (hydrodynamic dispersion, channeling),  and
diffusion.  Radioactive compounds can also decay. As
a result of sorption processes,  some solutes will move
more slowly than the ground water that is transporting
them; this effect is called retardation.  Biological
transformation, radioactive decay, and precipitation
will  decrease the concentration of the solute in the
plume but may not necessarily slow the rate of plume
movement. The following are the primary processes
that  affect  the  mobility  and   concentrations   of
radionuclides being transported by ground water:
                                                   4-36

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     !   Advection

     !   Dispersion

     !   Matrix Diffusion

     !   Retardation

     !   Radioactive Decay

Advection

The  process by which solutes are transported by the
bulk movement of water is known as advection.  The
amount of solute that is being transported is a function
of its  concentration in the ground  water and the
quantity of the ground water flowing.

Computer codes  that  account only  for  advective
transport and ignore dispersion and diffusionprocesses
generally  take  one of two approaches.   The  first
approach uses a semi-analytical method (Appendix C)
to solve the ground-water flow and transport equations,
whereas the second approach uses fully numerical
methods to determine the ground-water velocity field
from which directions and rates of solute movement
are calculated by the code.

The  semi-analytical method frequently fails when
aquifers are of complicated shape and nonhomogen-
eous. In these instances, it is better to use the second
option which utilizes a fully numerical code for deter-
mining the velocity distributions and particle (i.e.,
solute) paths. This may be accomplished with either
finite-differences or finite-elements (Appendix C).

Computer codes that consider only advection are ideal
for designing remedial systems (e.g., pump and treat)
because the  model  output  is in the  form of solute
pathlines (i.e.,  particle tracks)  which delineate the
actual  paths that  a  contaminant would  follow.
Therefore, capture zones created by pumping wells are
based solely on hydraulic gradients and are not subject
to  typical  problems  that  occur  when  solving
contaminant  transport  equations  which  include
dispersion and diffusion   in the  aquifer.   These
problems  are  numerical  dispersion  and artificial
oscillation.   Numerical dispersion  arises because
computers have a limited accuracy, thus some round-
off error will occur in the  computations.  This error
results in the artificial  spreading of contaminants due
to the  amplification of the dispersivity.  Hence,  the
contaminant will disperse farther than it should with a
given  physical,  or "real"  dispersivity.   This  extra
dispersion will result in lower peak concentrations and
more spreading of the contaminant.  Methods exist to
control  numerical  dispersion,   but the   methods
themselves  may   introduce  artificial  oscillation.
Artificial oscillation is the over-  or under-shooting of
the true solution by the model and results in inaccurate
solutions and  may give erroneously high  and low
concentrations.

There  are other ground-water  solute modeling  situa-
tions where the phenomenon of dispersion, together
with its many uncertainties, is only  a minor factor in
describing  the transport of radionuclides in ground
water and can be ignored.  For example, the flux of
contaminants entering a river that is recharged from a
contaminated  aquifer is   much less  sensitive   to
dispersion than the concentration in a particular well.
In the former case, the contaminated ground water
would  enter over a wide area, which would tend to
smear out the effects of dispersion. For similar reasons,
the transport from nonpoint sources of con-tamination,
such as mill tailings and large landfills, would diminish
the sensitivity of the modeled results to dispersion.  In
these instances, computer  codes that consider only
advection may be appropriate.

As mentioned previously,  advective codes  are also
excellent in the  remedial design stage for determining
the number and placement of extraction or  injection
wells and in evaluating the effect that low permeability
barriers may have on the flow system.  However, there
are a  number of  drawbacks  that must  be  carefully
considered when   selecting  a  code  that  ignores
dispersion and diffusion. The most significant of these
is that  matrix diffusion, which is discussed below, can
be one of the  most important processes  that will
determine the length of time that a pump and treat
system must operate before clean-up  goals will be met.
Without the ability to evaluate the effects of diffusion on
solute transport, it  would be very difficult to estimate
remediation times accurately.

A second potential problem with advection-based codes
is that dispersion will tend to spread contaminants over
a much wider area than would be  predicted if only
advective  processes  are   considered,   thereby
underestimating the extent of contamination. However,
because dilution is  under-accounted for, unrealistically
high peak concentrations are generally obtained, which
                                                  4-37

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may be  appropriate if conservative  estimates  are
desired.

Advective codes  also tend to yield more accurate
travel-time determinations of unretarded contaminants
because the  solution techniques are inherently more
stable, and numerical oscillations, which artificially
advance the contaminant front, are minimized.

Another important advantage of advective codes is that
the output (i.e., particle tracks)  is a very effective
means of ensuring that ground-water gradients, both
vertical  and horizontal,  are  consistent  with  the
conceptual model.

Hydrodynamic Dispersion

In the previous discussion, advective  processes  of
transport in porous media were presented.  In reality,
the transport of contaminants is also influenced by
dispersion and molecular diffusion, which is caused by
the tendency of the solute to spread out from the
path that it would be  expected  to follow if only
transported by advection (Figure 4-9). This spreading
of the contamination over an ever-increasing  area is
called    hydrodynamic  dispersion and   has  two
components: mechanical dispersion and  diffusion.
Hydrodynamic dispersion causes dilution of the solute
and occurs because of spatial variations
in ground-water flow velocities and mechanical mixing
during fluid advection. Molecular diffusion, the other
component of hydrodynamic dispersion, is due to the
thermal kinetic energy of solute particles and also
contributes  to the dispersion  process.   Thus,  if
hydrodynamic dispersion  is factored  into the solute
transport processes, ground-water contamination will
cover a much larger region than in the case  of pure
advection,  with a  corresponding reduction in  the
maximum   and  average  concentrations   of  the
contaminant.

Because  hydrodynamic  dispersion is  the   sum  of
mechanical dispersion and diffusion, it is possible to
divide the hydrodynamic dispersion term into the two
components  and have two  separate  terms in  the
equation. Under most conditions of ground-water flow,
diffusion is insignificant and is frequently neglected in
many of the  contaminant transport codes. However,
this artificial exclusion of the diffusion term may create
problems in certain instances as will be discussed under
the topic of matrix diffusion.

There is concern as to how adequately dispersion can be
represented in computer codes because it is related to
spatial scale and variations in aquifer properties which
are generally not explicitly simulated in the code (e.g.,
tortuosity).  Furthermore, dispersion coefficients  are
very difficult to measure in the field
                                                    DrS
 Figure 4-9.  Hydrodynamic Dispersion
                                                  4-38

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and are usually obtained during the model calibration
process.

These limitations suggest that not too much confidence
be placed in dispersion values, and that it is generally
best to use advection-dispersion-based codes to bound
the maximum probable extent that contamination may
have spread. However, as mentioned previously, peak
concentrations will tend to be underestimated.

Matrix Diffusion

Diffusion in solutions is the process whereby ionic or
molecular constituents move under the  influence of
their  kinetic  activity  in the  direction  of their
concentration gradient (Figure 4-10). The diffusion of
radionuclides from water moving within fractures, or
coarse-grained material, into the rock matrix or finer-
grained clays can be an important means of slowing
the  transport  of   the  dissolved   radionuclides,
particularly  for non-sorbing or low-sorbing soluble
species. The apparent diffusion coefficient for a given
radionuclide depends on properties that are intrinsic to
the chemical species (e.g.,  mobility)  as  well  as
properties of the rocks (such as porosity, tortuosity, and
sorption ratios).

As stated previously, matrix diffusion is  frequently
insignificant and  is often neglected in many of the
contaminant-transport codes.  However,  potential
problems arise when matrix diffusion is ignored and
contaminant  distributions  are  based  solely   on
advective-dispersive principles. For example, ground-
water pump and treat remediation systems work on the
premise that a capture zone is created by the pumping
well and all of the contaminants within the capture
zone will eventually flow to the well. The rate at which
the contaminants flow to the well may, however, be
very  dependent  on  the   degree   to  which  the
contaminants  have diffused into  the fine-grained
matrix (e.g., clays).  This is because the rate at which
they will diffuse back out of the fine-grained materials
maybe strongly controlled by concentration gradients,
rather  than the hydraulic  gradient  created  by the
pumping  well.   Therefore, matrix diffusion can
significantly retard the  movement of contaminants,
and, if the computer code does not explicitly account
for this  process, the overall effectiveness  of the
remediation system (i.e., clean-up times)  could be
grossly underestimated.

Other instances where matrix diffusion processes can
lead to  erroneous  model  predictions  is  in  the
determination of travel times, peak concentrations, and
flushing volumes.  The fact that  diffusion can play a
significant  role   in   slowing  the  transport  of
radionuclides suggests that, if it is  ignored, travel
rates,  as  well  as peak  concentrations,  will be
overestimated.    Frequently,  clean-up  times  are
estimated based on the flushing of a certain number of
pore  volumes.  However,  matrix  diffusion
                                                                 •in-',
                                                                 •j<>O.
Figure 4-10.  Matrix Dispersion
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processes, if unaccounted for, can cause the number
of required pore volumes to be greatly underestimated.
This is because pore volume calculations  generally
assume that water moves freely through all of the pores
and  does not  account for the  relatively stagnant
conditions of fine-grained rocks in which contaminants
may have diffused.

Retardation

In addition to the physical processes, the transport of
radionuclides is affected by chemical processes. The
following summary  of geochemical  processes that
could  potentially play  a role in the transport  of
radionuclides has been provided in order to offer an
appreciation of their wide variety and complexity:

     !   Sorption ~  the  attachment of  chemical
        species on  mineral  surfaces, such  as ion
        exchange,  chemisorption, van  der   Waals
        attraction, etc., or ion exchange within the
        crystal structure.

     !   Ion exchange phenomena ~ that type  of
        sorption restricted to interactions between
        ionic  contaminants and  geologic  materials
        with charged surfaces which can retard the
        migration of radionuclides.

     !   Speciation  ~ the distribution of a given
        constituent among its possible chemical forms
        of the  radionuclide which can influence  its
        solubility and therefore its rate of transport by
        limiting the maximum concentration of the
        element dissolved in the aqueous phase.

     !   Precipitation  ~  the  process  by   which
        dissolved  species exceed solubility   limits,
        resulting in a portion precipitating  out of
        solution.

     !   Natural colloidal formation ~ the attachment
        of radionuclides  to  colloids resulting in a
        mode of radionuclide transport or retardation
        which involves the movement or mechanical
        retardation of radionuclides attached to large
        colloidal paniculate matter suspended in the
        ground water or  the formation of colloidal
        clusters of radionuclide molecules.

     !   Radiolysis ~ the change in speciation due to
        radiation or recoil during radioactive decay,
        which   can  affect  the   solubility   of
        radionuclides.

     !   Biofixation ~ the binding of radionuclides to
        the soil/organic  matrix due to the action of
        some types of microorganisms  and plants,
        thus affecting mobility of the radionuclide.

     !   Natural  organic matter interactions ~  soil
        organic matter can play a significant role in
        mobilizing,  transporting,   sorbing,   and
        concentrating certain radionuclides.

     !   Anion exclusion ~ negatively charged rock
        surfaces can affect the movement of anions,
        by  either retarding the movement of anions
        by   not   allowing  negatively   charged
        radionuclides to  pass  through  the  pore
        opening, or by  enhancing the transport of
        ions by restricting the anion movement to the
        center of the pore channel where ground-
        water velocities  are higher.

Obviously, a wide range  of complex geochemical
reactions  can affect the  transport of radionuclides.
Many of these reactions are poorly understood and are
primarily  research topics. From a practical view, the
important aspect is the removal of solute from solution,
irrespective  of the process.  For  this reason, most
computer  codes simply lump all of the cumulative
effects of the geochemical processes into a single term
(i.e.,  distribution coefficient) which describes  the
degree to which the radionuclide is retarded relative to
the ground water. Thus, the distribution coefficient
relates the radionuclide concentration in solution to
concentrations  adsorbed to the  soil.  Because  the
distribution  coefficient is strongly  affected by  site-
specific conditions, it is frequently obtained from batch
or column studies in which aliquots of the  solute, in
varying   concentrations,   are  well   mixed   with
representative solid from the site, and the amount of
solute removed is determined.

If the sorptive process is rapid compared with the flow
velocity, the solute will reach an equilibrium condition
with the sorbed phase, and there is a greater likelihood
that the distribution coefficient approach will yield
reasonable values. However, if the sorptive process is
slow compared with the rate of fluid flow, the solute
may not come  to equilibrium with the sorbed phase
and geochemical (i.e., based on thermodynamics and
kinetics) models are generally required.
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Most computer  codes assume  that the distribution
coefficient is constant over all solute concentration
ranges  (i.e.,  linear  isotherm).    However,  this
assumption may place  a serious limitation  on the
predictive  capability  of the  code,  in that a linear
relationship between  the concentration  of solute in
solution and the mass of solute sorbed on the solid does
not limit the amount of solute that can be sorbed onto
the solid.  In actuality, this is not the case; there must
be an upper limit to the mass of solute that  can be
sorbed, due to a finite  number of sorption sites on the
solid matrix. This upper bound on sorption suggests
that, in a natural system, retardation would decrease as
contaminant  concentrations  in  the  ground-water
increase.  This discrepancy between computer codes
assuming linear sorption behavior when, in fact, non-
linear sorption is more accurate, can have important
implications when  predicting the migration of the
center of  mass versus  the  leading  edge  of  a
contaminant plume,  or when predicting required
pumping times for a pump and treat remedial action.
At  high concentrations,  the linear  assumption will
over-predict retardation and under-predict radionuclide
travel rates and contaminant concentrations.

A basic assumption in code  development is  that at
dilute concentrations the errors associated with using
linear  sorption   isotherms  to  predict non-linear
relationships will be minimal. However, radionuclides
present  a  special problem in that frequently  the
releases may be at dilute  concentrations but  over
extended durations.  These long time frames may allow
all of the sorption sites to be filled, even at low release
concentrations, and model results will diverge from
actual values by  under-predicting radionuclide travel
rates and concentrations.

The ability of a code to accommodate retardation
effects is essential for evaluating radionuclide transport
rates unless a special case is being considered,  such as
one involving tritium which moves unretarded or if the
primary  objective  is to  determine the  absolute
minimum travel times and maximum travel distances.
It is possible to back out travel rates and distances from
computer codes that do not accommodate distribution
coefficients; however, if the species are decaying, the
calculations can become very tedious.

Radioactive Decay

Radionuclides decay  to stable  products or to other
radioactive  species  called  daughters.   For some
radionuclides, several daughter  products may be
produced before the parent species decays to a stable
element. For some radionuclides, the daughter(s) may
present a potentially greater health risk  than the
parent.  Accounting for  the  chain-decay process is
particularly  important for predicting  the  potential
impacts  of  uranium,  thorium,  and transuranic
migration.

In considering this process over the transport path of
radionuclides, one transport equation must be written
for each original species and each daughter product to
yield the concentration of each radionuclide (original
species and daughter products) at points of interest
along  the  flow  path in  order  to estimate  total
radiological exposures.  However, not all computer
codes  that  simulate  radioactive  decay allow  for
ingrowth of the daughters, which may not cause  a
problem if the daughter half-lives are very long (i.e.,
they take a very  long time  to  grow  in) or  if the
daughter products are of little interest.  In addition, it
is computationally difficult to  account for ingrowth of
daughters during transport.   Codes that do address
daughter ingrowth generally account for ingrowth in
the contaminated zone only.  The difficulty arises in
the need to use the Kd of the daughter and changes in
the travel distance as the daughters  grow  during
transport through the unsaturated and saturated zones.

4.3.1.4  Multiphase Fluid Conditions

The movement of contaminants that are immiscible in
water  (i.e.,  non-aqueous phase  liquids  -  NAPL)
through the vadose zone and below the water table
results in systems which have multiple phases (i.e., air,
water,  NAPL).   This coexistence of multiple phases
can  be an important facet in many  contaminant-
transport analyses. However, only the  water and the
vapor  phase are of concern when evaluating the
transport of radionuclides.   A  limited number of
radionuclides can form volatile species that are capable
of being transported in a moving vapor or gas. Among
these are tritium, carbon-14, and iodine-129. Over a
large scale,  factors that  affect transport in flowing
ground water also affect transport in flow-ing gas (i.e.,
the velocity of the gas determines the potential for
advective transport). In the absence of flow, diffusion
is  the only mechanism for transport in the  gaseous
state.  The processes of partitioning of the volatile
species between the gaseous, liquid, and solid state and
isotopic exchange must  also  be consi-dered  when
assessing the impact of vapor transport.
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Currently a number of analytical and numerical codes
allow the investigation  of  vapor transport  in the
unsaturated zone; however, almost all of these codes
assume an immobile water phase. The limitation of
this assumption is that one of the principal concerns
regarding gaseous transport is its role in transporting
gas-phase radionuclides through the unsaturated zone
to the water table where  they may be dissolved and
transported  by  the  ground water.    Without the
capability to simulate the percolation of water through
the unsaturated zone, tritium concentrations reaching
the water  table will be greatly  underestimated.
Furthermore, remediation strategies cannot be fully
developed if the residual water held in the unsaturated
zone is assumed to remain stagnant.  For instance, a
method that has been proposed to remediate tritium
involves pumping the tritiated water from withdrawal
wells located downgradient from the source area.  The
contaminated water is subsequently reinjected  into
wells upgradient from the withdrawal wells.   In this
manner, tritium is recycled continuously until it decays
to levels below the remedial criteria (e.g., the drinking
water standards).  Two aspects  of this system that
could not be evaluated without having  the ability to
simulate  mobile water and vapor in the unsaturated
zone are, first, whether  vapor transport will carry
tritium beyond the limits of the hydraulic capture zone
created by the pumping wells, and second, what the
expected loading rates will be from the source term.

4.3.1.5  Flow Conditions

The ground-water environment can be divided into a
variably saturated (vadose zone) and saturated regimes.
The irregular surface that forms the boundary between
these two regimes is known as the water table.  Below
the water table, pressures are equal to or greater than
atmospheric and the  pores  and spaces within and
between individual soil particles are filled with water.
Above the water table, in the partially saturated zone,
water is generally under negative pressure or tension
(less than atmospheric).  Some of the pore space  is
usually occupied by gases derived primarily from the
atmosphere as well as pore water.

Radionuclide releases to the ground water may result
from a number of mechanisms.  These mechanisms
can affect ground water directly or indirectly, and they
include the following:

    !    Direct discharge  (e.g., on-site release from
        treatment processes)
     !   Leachate  generation  (e.g.,  from buried
        wastes,   surface  impoundments,   and
        absorption beds)

     !   Overland  flow  (e.g.,  from  impoundment
        overflow or failure, drum leakage)

     !   Contaminated   stream  interaction  with
        aquifers

The  decision as to whether the vadose zone and/or
saturated zone will be modeled is directly related to the
mechanism by which the contamination was released.
That is, if radionuclides are being released directly to
the water table, little would probably be gained by
modeling the  vadose zone.   However,  if the  risk
assessment   is  based   only   on  radionuclide
concentrations reaching the water table, it may not be
necessary to model the saturated zone.

After a determination is made as to whether the vadose
zone and/or saturated zone are to be modeled,  it
becomes  necessary to address a much more difficult
question, i.e.,  the complexity at which  each  zone
should be modeled.  This question can be answered
only by  attaining  a  thorough understanding of the
modeling objectives, as well as an appreciation of the
advantages and disadvantages  of each prospective
approach.

The sophistication of the unsaturated zone modeling
approach will  be based  primarily on  the overall
modeling objectives, although the complexity of the
hydrogeology may also play a significant role.  For
instance, accurate predictions of radionuclide flow and
transport through a very complex unsaturated zone
may be irrelevant and unnecessary if credit is not taken
for it in the baseline risk assessment.  On the other
hand, if the  risk  assessment is based solely upon
arrival times and peak concentrations of radionuclides
arriving  at the ground-water table, then a detailed
analysis of flow and transport through even a thin,
uncomplicated  unsaturated zone may  be significant
and require complex modeling.

Relative  to  saturated zone modeling, vadose  zone
modeling is characterized (plagued) by  significant
numerical   difficulties   and   greater  uncertainty
regarding conceptualization and parameter estimation.
In many  vadose zone modeling  situations, it may be
advisable to  use  simple  models and conservative
assumptions to estimate exposure concentrations.  The
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appropriate level of modeling and data collection for
risk   assessment   at  individual  sites  should  be
determined during the remedial process.

Situations may arise where reliable simulations of flow
and transport of radionuclides through the unsaturated
zone may not be possible even with complex ground-
water models.  In particular, if the unsaturated zone is
indurated with fractures or macropores with high
permeability, the flow and transport processes become
so involved that mathematical formulations of porous
media transport  are poor  representations of  the
physical phenomena. Furthermore, localized zones of
higher permeability may cause the  wetting front to
advance at highly variable rates, which may introduce
significant disparities between the actual and predicted
contaminant concentrations.

Under single-phase flow conditions, an option to select
a vadose zone code which simulates hysteresis is
provided. Hysteresis is simply a term which describes
the fact that wetting and drying curves for a certain
soil (pressure head versus volumetric water content),
under partially saturated conditions, are not the same.
That is, the pressure head is not only dependent upon
the water content but also on whether  water is being
removed or added to the system.  The effect is due to
both the geometric shapes of the pores and the contact
angle between the water and the mineral  surface,
which is different depending on whether the water is
advancing and retreating. Of particular relevance in
considering hysteric effects as a code-selection criteria
is that hysteresis will have little effect on the flow and
transport  of contaminants.   The  primary  utility of
including hysteresis is to account  for this process
during model validations  studies.  Therefore, if model
validation will not be performed, which will be  the
case in the vast majority of modeling  studies,  the
capability of a code to  simulate hysteresis will be of
little importance.

4.3.1.6  Time Dependence

The most frequently performed ground-water modeling
is that of the saturated zone. The parameter needs are
well defined and the field data collection activities are
relatively straightforward.   The major  factors that
provide immediate insight into whether sophisticated
ground-water modeling  will be  necessary  are  the
complexity of the:

    !   Source term
     !   Dominant flow and transport processes
     1   Hydrogeology (e.g., layers, heterogeneity)
     I
        Hydraulic boundaries
Previous discussions  have  addressed the  relative
importance  of these  issues  in  the  code selection
process.  However, one aspect that has not been fully
considered is the temporal nature of flow and transport
within  the   system.    As  discussed   previously,
simulations can be performed in either a  steady or a
transient state.  At steady-state, it is assumed that the
flow field and contaminant releases remain constant
with time, whereas a transient system simply means
one that fluctuates with time. This fluctuation may be
induced by  both natural  (e.g.,  tides, rainfall) and
manmade influences (e.g., wells, hydraulic barriers).
In many instances, transient systems, if observed over
the long term,  will approach relatively  steady-state
conditions.

As far as code selection is concerned, relative to the
temporal  behavior  of the  system,  it  is  a fairly
straightforward decision.  Namely, most analytical
models  do  not  simulate  a transient flow  system;
therefore, if a transient  flow system needs to be
modeled, analytical and semi-analytical methods are
generally not available. Furthermore, if a steady-state
flow system is acceptable, but a transient transport
capability is required, both analytical and numerical
codes are readily available for these conditions and the
selection  criteria  should  be   deferred  to  other
considerations.

4.3.2   Code-Related Characteristics

In addition to the site-related characteristics presented
in the previous section, the code selection process must
also consider attributes that are integral components of
the computer code(s), including:

         !    Geometry

         !    Source Code Availability

         !    Code Accessibility/Ease of Use

         !    Code Verification and Validation

         !    Code Output

         !    Solution Methodology (Appendix C)
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4.3.2.1  Geometry

The decision to model a site in a particular number of
dimensions should be based primarily upon both the
modeling objectives and the availability of field data.
Other considerations include whether a computer code
exists that can simulate the dominant processes in the
desired number of dimensions, and whether hardware
requirements are compatible with those available.

In determining how many dimensions are necessary to
meet the objectives,  it becomes necessary to gain a
basic  understanding of how ground-water flow and
contaminant  concentrations  are  affected by  the
exclusion or inclusion of an additional dimension. It
should be kept in mind that the movement of ground
water and contaminants  is  usually  controlled by
advective  and  dispersive  processes   which  are
inherently three-dimensional.   Advection is more
responsible for the length of time (i.e., travel time) it
takes for a contaminant to travel from the source term
to a downgradient receptor, while dispersion directly
influences the concentration of the contaminant along
its travel path.  This fact is very important in that it
provides  an  intuitive  sense  for  what   effect
dimensionality has on contaminant migration rates and
concentrations.   As  a general rule,  the fewer the
dimensions,  the  more  the model results will over-
predict concentrations and under- predict travel times.
Concentrations  will  be  over-  predicted  because
dispersion, which is a three-dimensional process, will
be dimension limited and will not occur to the same
degree as it actually would in the field.  Travel times
will be under-predicted, not because of a change in the
contaminant velocities, but because  a more direct
travel path  is  assumed.    Therefore,  the  lower
dimensionality models tend to be more conservative in
their predictions and are frequently used for screening
analyses.

One-dimensional simulations of contaminant transport
usually   ignore  dispersion  altogether,   and
contamination  is  assumed  to migrate  solely  by
advection, which results  in  a highly  conservative
approximation. Vertical analyses in one dimension are
generally reserved for evaluating flow and transport in
the unsaturated zone.

Two-dimensional analyses of an aquifer flow system
can be performed as either a planar  representation,
where flow and transport are assumed to be horizontal
(i.e., longitudinal and transverse components), or as a
cross section where flow and transport components are
confined to vertical and horizontal components.  In
most  instances,   two-dimensional  analyses  are
performed in an areal orientation, with the exception
of the  unsaturated zone,  and are  based on the
assumption that most contaminants enter the saturated
system from above and that little vertical dispersion
occurs. However, two-dimensional planar simulations
have a  number of limitations.  These include the
inability to simulate multiple layers (e.g., aquifers and
aquitards) as well as any partial penetration effects.
That is, the contaminant source, wells, rivers, lagoons,
and  lakes are  all  assumed to  penetrate the  entire
thickness of the aquifer. Furthermore, because vertical
components of flow are ignored, a potentially artificial
lower boundary on contaminant migration has been
automatically assumed which may or may not  be the
case.

A two-dimensional formulation of the flow system is
frequently  sufficient   for  the purposes  of  risk
assessment, provided that flow and transport  in the
contaminated aquifer are essentially horizontal.  The
added complexities of a site-wide, three-dimensional
flow and transport simulation  are often  believed to
outweigh the expected improvement in the evaluation
of risk.   Complexities  include  limited  site-wide
hydraulic head and lithologic  data with depth and
significantly increased computational demands.

Quasi-three-dimensional analyses remove some of the
limitations that are inherent within two-dimensional
analyses.   Most notably,  quasi-three-dimensional
simulations allow for the incorporation  of multiple
layers; however, flow and transport in the aquifers are
still  restrained to  longitudinal  and   transverse
horizontal components, whereas flow and transport in
the aquitards are even further restricted to vertical flow
components only. Although partial penetration effects
still  cannot   be   accommodated  in  quasi-three-
dimensional analyses,  this  method can sometimes
provide a good compromise between the  relatively
simplistic two-dimensional analysis and the complex,
fully three-dimensional analysis.  This is the case,
particularly if movement of contaminants from the
shallow aquifer through a confining unit and  into a
deeper aquifer is suspected.

Fully three-dimensional modeling  generally allows
both the geology and all of the dominant flow and
transport  processes  to  be   described   in   three
dimensions. This approach usually affords the most
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reliable means of predicting ground-water flow and
contaminant transport characteristics, provided that
sufficient representative data are available for the site.
Fully three-dimensional analyses are often the only
defensible means to evaluate the effectiveness of many
potential remedial scenarios. For example, extraction
and  injection  wells  may  create  strong vertical
gradients, as well as three-dimensional capture zones.
Without the ability  to accommodate these gradients
and capture zones, dilution effects and capture zones
could be over- or underestimated.  The ground-water
flow and contaminant transport beneath a barrier wall
would also be subject to serious predictive limitations
without a three-dimensional analysis, againbecause of
the strong vertical gradients that generally accompany
these features.

4.3.2.2  Source Code Availability

As a general rule, an effort should be made  to use
publicly available computer codes, provided they have
been well documented and tested and can meet all of
the major requirements of the modeling objectives. In
certain  instances, however, it may  be  necessary to
purchase a proprietary code.  A proprietary  code may
be needed for  a  number  of  reasons, but,  most
commonly, proprietary  codes  are selected  either
because the user is familiar with the code or because
the publicly  available codes would not  meet the
modeling objectives.

The  following  is a list of factors  that need to be
considered during  the  selection process  of both
proprietary and non-proprietary computer codes:

     !   Whether the code has been widely used and is
        generally  accepted   by  the   technical
        community;

     !   How  well the code  is  documented  and
        verified;
     !   Whether the code has been independently
        peer reviewed;

     !   Whether the purchase  price  of the  code
        provides any technical support, and,  if
        additional support is required, what it will
        cost;

     !   Whether the source code is provided, and, if
        not,  under  what  conditions  could  it be
        obtained if necessary;

     !   Whether the code has ever been applied to a
        similar problem with consistent objectives;

     !   Whether the code has been field tested on
        problems directly relevant to the subject site;

     !   Whether the code has  ever been used to
        support a case  in litigation or  regulatory
        enforcement action;

     !   Whether any additional enhancements or
        modifications to the code are planned in the
        future.

4.3.2.3  Code Testing and Processing

The verification process is generally undertaken during
the developmental stages of the computer code. It is a
procedure in which  analytical equations of known
solutions are used to ensure that there is an agreement
between the formulations and solutions of the  same
basic equations, which are solved with more complex
numerical methods.   In  some instances, numerical
methods, which have been verified with  analytical
solutions, are used to check other newly formulated or
even more complex numerical solutions.  The purpose
of verification is to show  only  that the numerical
techniques work and that no errors exist in either the
mathematical formulation or in the actual coding of
the formulation.

One important aspect of code verification is that it can
usually  be performed independently   of  the  code
development process.  This allows  the accuracy of
codes to be checked even without access to the source-
code documentation. It is not recommended, however,
that codes be selected that were not verified during the
development process and are not well documented.
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Calibration and validation are activities designed to
test the realism of the ground-water flow and transport
model. From a philosophical perspective, calibration
and validation are very different. When addressing the
subject of calibration, it is generally assumed that both
the conceptual  model  and  numerical models are
reasonably correct or adequate. Therefore, to calibrate
a model, model parameters are simply adjusted within
an   acceptable  range,  based   on   site-specific
measurements, to arrive at a best fit of the dependent
variable,  which is usually hydraulic head or solute
concentrations.   Validation, on the  other hand,
examines  in more detail the realism  of both the
conceptual model and the numerical model.

Model calibration of vadose zone models  is very
difficult and rarely attempted primarily due  to data
limitations, whereas calibration of saturated flow and
transport models is relatively straightforward, provided
there  are sufficient field measurements of hydraulic
head  or  solute-concentration data.   One potential
problem with calibration of saturated flow models is
that  a  unique  solution  for the  hydraulic  head
distribution  is  not  available  if all  of the boundary
conditions are either no-flow or fixed head.  In other
words, if the model does not contain a flux condition
of significant magnitude (relative to total flux through
the model), increasing or decreasing all the hydraulic
conductivities  in equal proportion will result in the
exact same  hydraulic head  distribution.  The only
difference is that the amount of flux through the model
will be increased or decreased in proportion to the
change in hydraulic conductivities.  This is why  it
becomes very  important to not only narrow the
probable  ranges of hydraulic conductivities through
methods  such as aquifer tests but also to use mass
balance information to check the calibration results.

Model validation is, in general, a comparison of the
solutions of the mathematical equations from which
the model is formulated  with field-measured data.
Compelling arguments have been made that ground-
water models  cannot be validated,  only invalidated
(KON92). Accordingly, validation is best thought of
as a process for determining the degree to which a
model can  be relied  upon to   support a  specific
modeling objective at a specific site.  Validation, at
best, may consist of reasonable agreement between
simulated results and actual field data at two or more
time periods.
Attempts to validate models must address the issue of
spatial variability when comparing model predictions
with limited field observations. If sufficient field data
are obtained to derive  the probability distribution of
contaminant concentrations, the results of a stochastic
model can be compared directly. For a deterministic
model, however, the traditional approach has been to
vary the  input  data within  its  expected range of
variability (or uncertainty) and determine whether the
model results fall within the bounds of field-measured
values.

Regardless of whether the solution is  obtained by
analytical or numerical techniques, true validation or
history matching canbe done only through comparison
with field measurements and, in some cases, laboratory
data.  Furthermore, given the lack of comprehensive
field data sets  that adequately describe the spatial
parameter distributions, and our inability  to directly
measure water and  solute fluxes which are more
logical variables for model validation, it is highly
unlikely that complete validation  of any  simulation
model canbe possible.

Such complete validation, however,  is not necessary
for most modeling approaches if model limitations are
adequately recognized.  It should also be kept in mind
that validation  is site-specific and consequently its
utility, if achieved at one location,  is limited when
considering application of the  model at  another
location.

The need for the overall validation or history matching
outlined above is directed at the creation of reasonably
reliable computational and forecast capabilities for
studies that would generally go beyond the baseline-
risk assessment.  It  is  acknowledged that the field
testing efforts outlined here usually occur concurrently
with the remedial process; however, validation or field
testing  is not simply  applying models within the
remedial investigation  context.  This is because the
remedial investigation  of a waste  site may strongly
focus on the calculation of risk.  For example, if all
contaminants released at a waste site are immobile, the
remedial  investigation  activities in support of the
baseline  risk assessment may  concentrate on the
quantification of partitioning between the water and
the solid phase.  As such, simplified flow and transport
models may be  used  to support  the baseline  risk
assessment under this situation.  Within this context,
it is recognized that flow and transport modeling is
only one component of the risk calculation, and those
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responsible for the quantification of the baseline risk
assessment may employ a relatively unsophisticated
modeling approach for the baseline and perhaps very
conservative simulations. On the other hand, for other
situations, detailed flow and transport analyses may be
required.  Under these conditions, resolution of the
flow and transport model validation issue will require
examination of the waste site with models of some
complexity  or sophistication  with regard to  the
geologic structure and dominant processes.

4.3.2.4  Model Output

One aspect of the computer code that is frequently
ignored in the selection process is the form that the
model output will take.   It is true, however, that in
most instances the actual output can be fashioned into
the  desired format, provided  the  model  itself is
consistent with required output.  That is, output in
three dimensions  cannot be obtained  with a two-
dimensional model.

In general, the model output is expressed in terms of
hydraulic head, pressure, or solute concentrations. The
spatial coverage of parameter output values is  either
dependent  on the  frequency  of  nodal   spacing
(numerical)  or on the number  of specified x and y
coordinates  (analytical) which are  included in  the
model input files.  Code output will also vary due to
the inherent nature of the code itself. For example,
codes that simulate movement in the unsaturated zone
produce what  are  termed saturation profiles. These
profiles indicate what percentage of the pore space is
filled with water, whereas saturated zone codes have
no need for this capability because all of the  pores
below the water table are assumed to be filled.

Some codes provide output in a format which is very
useful and saves time during the post-processing of the
data. The best example of this  is where the user  can
specify nodes where concentration profiles are desired
with time (i.e., breakthrough curves). These profiles
allow  arrival  times,   peak   concentrations,  and
contaminant mass changes to be easily evaluated.
The  single most important code selection  criteria,
relative to the model output, would be that the code
provides mass-balance information.  A mass-balance
determination is a check to ensure that at steady-state,
the amount of water or contaminant mass entering the
system equals the amount exiting the system. If inflow
does not equal outflow for a steady-state  simulation,
there may be  something wrong with  the numerical
solution, although errors in the mass balance may also
indicate that there are problems with the mass balance
formulation   itself.     Therefore,   mass-balance
information not  only  provides a  check  on  the
mathematical formulations within the code, but it also
assists in ensuring that input parameter conversions
and other errors have not been made.

It is  not uncommon for codes that do  include mass-
balance output to provide information (e.g., fluxes,
heads) on specific boundaries  as well  as the source
term, all of which can be used in the interpretation and
evaluation of the predicted flow  and solute transport
directions and rates.

4.4 MODELING DILEMMAS

The  previous sections have described how site- and
code-related  features  affect the  model selection
process.   What  is not presented, however, is  a
discussion of the processes that are very difficult, if not
impossible, to model with currently available  models.
Complex flow and transport processes present another
difficulty in that computer codes currently do not exist
that  explicitly accommodate  a number of  these
processes including:

     !   Turbulent Ground-Water Flow

     !   Facilitative Transport

     !   Unsaturated Fracture Flow

     !   Complex Geochemical Reactions

Although these  processes  are very complex, it is
important that at least a basic understanding  of these
mechanisms and concepts be grasped prior to initiating
field or modeling investigations in which they may be
important.  The subsequent discussion will introduce
the difficulties associated withmodeling these complex
processes. Of particular relevance is that the processes
are not fully understood and are, therefore, not well
described mathematically.  If modeling is not possible
                                                   4-47

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because  of  the  overall  complexity  of  the  site
characteristics, it is common for a greater emphasis to
be placed on empirical rather than predicted data.
This may involve establishing long-term monitoring
programs, which in effect, have objectives similar to
those of ground-water modeling.

Turbulent Ground-Water  Flow.   As ground-water
velocities increase,  flow diverges from the laminar-
type which  is characteristic  of low velocities  and
becomes more turbulent.   At the point in which
turbulent flow is reached,  a basic law describing the
relationship between hydraulic gradient and specific
discharge (i.e., Darcy's) breaks down and is no longer
valid.   Most ground-water flow, however, is  not
turbulent, except in the very close proximity of large
pumping or recharging wells.  In practice, however,
turbulent flow over relatively small areas is generally
ignored without introducing any severe limitations in
the modeling.  On the other  hand,  in cases where
turbulent flow is observed over relatively large areas,
such as cavernous limestone aquifers, Darcy's law may
be significantly violated and results from flow  and
transport modeling would be of questionable value.

Facilitative  Transport of Radionuclides.  Field  and
laboratory investigations have indicated that  under
certain conditions contaminants are more mobile than
would  be predicted based  on  properties  such as
solubility,   ion   exchange,    speciation,   sorption-
desorption  and  ground-water velocities.    These
predictions,  however,  have not  accounted for the
potential   interactions  between   the  inorganic
contaminants  and mobile colloids.   Colloidal-size
particles include humic substances, clay minerals, iron
oxides and microorganisms. Colloids not only have a
high surface area per unit mass and volume, but many
types of colloids are also extremely reactive sorbants
forradionuclides. Therefore, radionuclides that might
otherwise be  sorbed  to  stationary material in the
aquifer could be transported in the sorbed  layers of
these mobile  colloids.   Sorption in this  case  has
facilitated transport.

A number of actinides, plutonium in particular,  can
form natural colloids under conditions of near-neutral
solutions of low ionic strength.  It is also suspected that
americium may form colloids under similar conditions.
Colloidal particles (up to 0.5 micrometers in diameter)
remain  suspended for long periods and hence may
migrate with the ground water.  As the solid  waste
form is leached, particles containing radionuclides may
form by the sorption of dissolved radionuclides on
nonradioactive particles. At this time it is believed
that plutonium and americium are most likely to be
transported as colloids,  although other radionuclides
might be subject to this transport process under certain
conditions.   Transport  of particulates in geologic
media will depend on aqueous flow rate, on pore and
fracture size in the rock, on ions carried in the water,
and on the nature  of the paniculate matter.  Several
mechanisms may remove colloidal particulates from
ground water such as mechanical filtration by the rock
matrix,  sorption on the surface of the rock pores (van
der Waals), and neutralization of the repulsive charges
on the colloids, thus allowing them to coagulate.

Radiocolloids may arise from a variety of sources. The
corrosion of metal containers can lead to the formation
of absorbent colloids.  Degradation of engineered
backfills may also  lead to colloidal formation.  If the
waste form is leached  by ground water,  naturally
occurring   colloids   derived   from  smectites,
vermiculites, illites, kaolinite, and chlorite present in
ground water may  also adsorb radionuclides.

The degree to which facilitative transport can be
modeled is largely dependent upon the objectives of the
modeling and the extent of understanding of the
transport mechanisms active at the site. A site-specific
evaluation may be required to determine the possible
importance of colloidal transport on the mobility of the
radionuclides.     To   estimate   the   amount   of
radionuclides that could be  transported by colloidal
suspension, it is first necessary to determine whether
colloidal-sized particles  exist in  the ground water.
Then, the sorption ratios for waste elements on these
particles must be  measured or estimated from the
composition  of the  particles.    In addition,  the
conditions under which  colloids could form from the
waste elements or from the waste  and their stability
after formation must be determined.   Finally, the
conditions necessary for the filtration or sorption of the
particles by the rock matrix itself must be defined.

An alternative approach to detailed site investigations
to characterize the potential for  colloidal  transport
would be to undertake a conservative approach and set
all  of  the distribution  coefficients  to  zero.   This
approach, however, may not always be conservative in
that it is possible that  under certain circumstances
colloids may have  a velocity greater than the average
linear ground-water velocity. This may be due to both
size-exclusion and charge-repulsion.  Size-exclusion
                                                   4-48

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occurs when molecules or ions are so large that they
cannot be transported through the smaller pores. As a
result, they are restricted to the larger pores, in which
the ground-water velocity is greater than average. The
charge-repulsion phenomenon  occurs  when  the
colloids have a negatively  charged  surface which is
repelled by the negatively charged clays which line the
pore channels. This process may confine the colloid to
the central part of the channel where the velocities are
highest and  the ground-water velocity is greater than
average.

Attempts have also been made to model the transport
of colloids  which are more mobile  than water  by
setting the distribution coefficient to  less than zero.
This approach, however, has a number of problems.
One of the most significant of these is that all of the
waste released from the source term would be assumed
to be transported as colloids which may result in overly
conservative solutions.

Currently, ground-water models do  not exist that
describe the constitutive relationships involved with
colloidal transport  and  explicitly  account  for the
dominant geochemical  interactions responsible for
colloidal transport.

Unsaturated Fracture Flow.  As previously discussed,
ground-water  modeling of the unsaturated  zone is
based upon developing sets of moisture-characteristic
curves, that is the functional  dependence of liquid-
water saturation and relative hydraulic conductivity on
the liquid-water potential within the rock matrix and
fractures for each hydrogeologic unit.  In unfractured
rocks, these  relations  refer to the storage and
movement of liquid water within  and  through the
interstitial pore space.  In fractured  rocks, allowance
must be made for the storage and movement of water
within the interconnected fracture openings as well as
for the movement  of water  between  the  fracture
openings and the rock-matrix pore  space.  Standard
field and laboratory methods are not yet available by
which  to   determine  the  moisture-characteristic
relations for fractures within the unsaturated zone.

Liquid-water  storage within  fractures  probably is
insignificant, but the flow of liquid  water within and
across fractures is not yet well understood.  Theoretical
models for  liquid-water flow in single unsaturated
fractures have been developed but have not yet been
field tested.  Fractures may or may not impede liquid-
water flow at low matrix saturations, and longitudinal
flow within the fractures may dominate liquid-water
flow  above  some   critical   matrix  saturation.
Consequently, at high  matrix  saturations,  fracture
systems and fault zones may become highly  efficient
pathways for liquid-water flow.  Liquid-water flow
within fractures may or may not be  Darcian (i.e.,
laminar) and will be dependent on the gradient and
hydraulic conductivity.

At low  matrix saturations, little or no water moves
longitudinally within the fracture openings, and the
effective hydraulic conductivity is controlled by that of
the fracture-bounded matrix blocks.  As the matrix
approaches   complete  saturation,  however,  the
movement  of water within and along the  fracture
aperture rapidly becomes more efficient  so that at
complete saturation the fractures may be dominant
contributors to the net hydraulic conductivity.  The
relative  contributions of fractures and matrix to the net
effective hydraulic conductivity depend on the fracture
frequency,  aperture-size distribution, and degree of
interconnectivity. However, there is currently no way
to generate a complete set of fracture location and
geometry data.

In essence,  a generally poor understanding of the
physics  controlling fluid flow in fractured-unsaturated
systems,  in  conjunction with  an  inability  to
characterize  the  fracture  properties and  locations,
makes it nearly  impossible to model these  systems
reliably.

Complex Geochemical Reactions. Radionuclides are
undergoing  geochemical  reactions.   The principal
geochemical   properties  and   processes   of  the
radionuclides,  which   may  be  site-specific  and
important to understand, include the following:

     !   Complexation

     !   Phase transformations

     !   Adsorption and desorption

     !   Precipitation

As stated previously, if it is  desired to model these
processes explicitly, as opposed to  using simplifying
assumptions such as default or aggregate retardation
coefficients,  geochemical rather  than flow  and
transport models may be required. As indicated, some
of the more common radionuclides, such as uranium
                                                   4-49

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and plutonium,  can exist in a number of chemical
states, which can significantly affect their  rate of
transport.  Other radionuclides, such as tritium, are
relatively insensitive to the site geochemical conditions
but undergo phase transformations which are difficult
to simulate with existing codes. Explicit geochemical
models can be  applied  to  assist in  evaluating the
general effect that the geochemical environment will
have on the radionuclide fate and transport, but even
these methods are often unreliable and the results must
be interpreted carefully.
                                                   4-50

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                                             SECTION 5
                               THE CODE SELECTION PROCESS
Section 4 described the various waste and site characteristics and processes and the code-related characteristics
pertinent to the code selection process.  The emphasis was placed on recognizing when specific waste, site, and code
characteristics are important and therefore must be considered in order to meet the modeling needs of each phase of
the remedial process. This section presents the basic procedure that should be followed in evaluating ground-water
flow and transport code(s) prior to making a final selection among two or more potential codes.
5.1 OVERVIEW OF THE CODE REVIEW AND
    SELECTION PROCESS
          Verification
          Validation
Given that an investigator understands  the various
waste and site characteristics that need to be modeled
in order to meet specific modeling objectives, there
will often be several suitable computer codes  which
could potentially be chosen from a large number of
codes published in the scientific literature (BAC80,
EPA91, and MOS92).  As mentioned in Section 1,
IMES "Integrated Model Evaluation System" provides
an excellent computerized means by which codes may
be  screened  automatically  for their  respective
capabilities.  The user simply checks off the desired
code capabilities within a screening module of IMES,
and the program eliminates all of the codes without the
specified  capabilities from an  extensive internal
database.   Furthermore,  IMES  will provide some
information  on the  code  itself  although  these
descriptions are, in many instances, somewhat limited.
Ideally, a detailed evaluation of each candidate code
should be performed to  identify   the  one most
appropriate  for the  particular  site  and  modeling
objectives.  The resources to complete a detailed study
are seldom available, and usually only one to two codes
are selected based upon a cursory  review of code
capabilities. Regardless of whether a detailed or more
cursory review is performed, it is important for the
reviewer to be cognizant of the following factors and
how they will affect final code selection:

    1.   Code Capabilities Consistent with:
          User needs
          Modeling objectives
          Site characteristics
          Contaminant characteristics
          Quality and quantity of data
    2.   Code Testing
          Documentation
    3.   History of Use Acceptance

The  first aspect of the review concentrates on the
appropriateness of the particular code to meet the
modeling  needs of  the  project.  This  subject  is
discussed in depth in Sections 3 and 4. The reviewer
must also determine whether the data requirements of
the code are consistent with the quantity and quality of
data available from the site.  Next, the review must
determine whether the code has been properly tested
for its intended use.   Finally, the code should have
some history of use on similar projects, be generally
accepted within the  modeling  community, and be
readily available to the public.

Evaluating a code in each of the three categories would
take  a significant effort, especially with respect to code
testing.  Theoretically, the reviewer should obtain a
copy of the computer code, learn to use the code, select
verification problem  sets with known answers, and
compare the  results of the model to  the benchmark
problems.  This task is complicated, largely because no
standard set of benchmark problems exists, and the
mathematical formulation for each process described
within the  code has  to be  verified  through the
benchmarking process.  Primarily for this reason,
selection of codes that are already widely tested and
accepted is recommended.  Code validation,  which
involves checking the model predictions against actual
field investigations designed specifically  to test the
accuracy of the model, would almost never be practical
during the code evaluation and selection process.

The  selection and evaluation process presented in this
section takes an approach which is consistent with
industry standards by relying on published reports and
user interviews as a substitute for actual hands-on
testing.  The result is a code selection and evaluation
                                                   5-1

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process that provides a reasonable technical review
that is relatively straightforward and takes a relatively
short time to complete (Figure 5-1).

The model evaluation process presented in subsequent
sections involves the following steps:

    1.   Contact the author or curator of the code and
        obtain the following:

        Documentation  and  other  model-related
        publications

        List of users

        Information related to code testing

    2.   Read all publications related to the model,
        including documentation, technical papers,
        and testing reports.

    3.   Contact code users to find out their opinions.

    4.   Complete the  written evaluation using the
        criteria shown in Table 5-1.

Much  of the information needed  for a thorough
evaluation can  be  obtained  from  the author  or
distributor of the code.  In fact, inability to obtain the
necessary publications  can indicate that the code is
either not well documented  or not widely used.  In
either case, inaccessibility of the documentation and
related publications should be grounds for evaluating
the code as unacceptable.

Most of the items in Table 5-1 should be described in
the code documentation, although excessive use of
modeling jargon  may make some items difficult to
find.   For this  reason, some assistance from an
experienced modeler may be required to complete the
evaluation. Detailed conversations with users can also
be  used   to  decipher  cryptic  aspects   of  the
documentation.

The evaluation process recommended in the following
sections  relies  on  user opinions  and  published
information to take the place of hands-on experience
and testing.  User opinions are especially valuable in
determining whetherthe code functions as documented
or has  significant errors (bugs).  In some instances,
users  have   performed  extensive   testing   and
benchmarking or are familiar with published papers
documenting the use of the  code.  In essence, the
proposed evaluation process substitutes second-hand
experience for first-hand knowledge (user opinions) to
shorten the time it takes to perform the review.  It is
also important to keep in mind that code selection is a
very dynamic process, and multiple codes may need to
be selected over the  remedial lifetime of the site in
order not only  to  reflect the remedial phase of the
project, but  also  to  remain current  with existing
technology.

Models attempt to simulate natural processes through
a series of mathematical expressions.  Because of the
simplifications  and assumptions needed to simulate
these  processes,  all  models will be inexact  and
imprecise.  Thus,  it  is important to understand the
magnitude of these deficiencies prior to the selection
and/or application of any model. As a first step in this
process, available documentation on the model must be
reviewed and evaluated to determine if the documented
capabilities of the model correspond with the objectives
of the study.  Code documentation is, however, often
biased and in many cases incomplete.  Furthermore,
major inherent weaknesses of the code (e.g., omission
of a process such as daughter in-growth) may not be
highlighted. For this reason, it is important to secure
or prepare independent reviews of any code before it is
selected.   These reviews can be  obtained from the
literature  and   supplemented  with   code-specific
evaluations similar to those presented in this report.
To the extent possible, the code should be exercised
with representative data prior to  its final selection.
Failure to conduct such audits and benchmark testing
may result in the inappropriate selection of a code and
in a waste of time and resources.

As  the user friendliness of the codes increase, the
practical expertise of the user typically decreases.  This
is a potentially dangerous situation because of the large
potential for code misuse. In prior years when codes
were available only in mainframe-type environments,
they were almost always used by  "experts" who had
knowledge of the capabilities of a selected code. Based
on this knowledge, appropriate inputs would be  used
in a modeling effort.  Now,
                                                   5-2

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                                  Project Manager
                                        and
                               Technical Support Staff
                               Development of Relevant
                                Code Selection Criteria
                        Based on Site and Code Characteristics
                                  (Sections 3 and 4)
                   Preliminary Screening of Potential Computer Codes
                                     (e.g. IMES)
Evaluate Relative
  Importance of
    Criterion
      Is
   Criterion
   Critically
  Important?
Does Code Meet
   Criterion?
                                  Enter Attribute into
                                Code Capability Table
                                    (Appendix D)
                               Preliminary Identification of
                                 Potential Code(s) That
                                 Meet Critical Criterion
                               Detailed Code Evaluation
                                 and Final Selection
                                     (Chapter 5)
                Contact Author
Review Relevant
  Publications
  Contact
Code Users
                                  Document Findings
                              FINAL CODE SELECTION
    Figure 5-1.  Code Selection Review Process
                     5-3

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                   Table 5-1.  Model Selection Criteria
                                  CRITERIA
Section 5.2.1 Administrative Data
                Author(s)
                Development Objective (research, general use, education)
                Organization(s) Distributing the Code
                Organization(s) Supporting the Code
                Date of First Release
                Current Version Number
                References (e.g., documentation)
                Hardware Requirements
                Accessibility of Source Code
                Cost
                Installed User Base
  	Computer Language (e.g., FORTRAN)	
Section 5.2.2 Remedial Process
                Scoping
                Characterization
                Remediation
Section 5.2.3 Site-Related Criteria
                Boundary/Source Characteristics
                    Source Characteristics
                        Multiple Sources
                        Geometry
                            line
                            point
                            area
                        Release type
                            constant
                            variable
                Aquifer System Characteristics
                    confined aquifers
                    unconfined aquifers (water-table)
                    aquitards
                    multiple aquifers
                    convertible
                Soil/Rock Characteristics
                    heterogeneity in properties
                    anisotropy in properties
                    fractured
                    macropores
                    layered soils
                Transport and Fate Processes
                    dispersion
                    advection
                    diffusion
                    density dependent
                    partitioning between phases
                        solid-gas
  	solid-liquid	
                                      5-4

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                                       Table 5-1.  (Continued)
                                               CRITERIA
                                 equilibrium isotherm:
                                    linear (simple retardation)
                                    Langmuir
                                    Freundlich
                                    nonequilibrium isotherm
                                 radioactive decay and chain decay
                                 speciation
                         Multiphase Fluid Conditions
                            two-phase water/NAPL
                            two-phase water/air
                            three-phase water/NAPL/air
                         Flow conditions
                            fully saturated
                            variably saturated
                         Temporal discretization (steady-state or transient)
            5.2.4      Code-Related Criteria
                         Source Code Availability
                         History of Use
                         Code Usability
                         Quality Assurance
                            code documentation
                            code testing
                         Hardware Requirements
                         Solution Methodology
                         Code Output
              	Code Dimensionality
default values are available, and it is possible for a user
with only limited knowledge to produce a result. This
result may, however, be highly inaccurate, and the user
may be unaware of potential errors.

5.2 EVALUATION CRITERIA

The code(s) to be used for a particular application will
satisfy a  combination  of needs defined by the
intersection   of  regulatory   requirements,   site
characteristics, and attributes of the code (Figure 5-2).
The code review process outlined  within the next
sections is based upon a complete and consistent set of
evaluation criteria. The evaluation process follows a
scheme which groups evaluation criteria based on their
similarity  to one another.  That grouping is reflected
in the organization of Table 5-1.  Yet the selection
process must also account for the interrelationships
between evaluation criteria.  For example, certain
groups of criteria will influence model selection and
evaluation in different  ways.    Some  criteria are
important in  choosing  among  codes,  others  in
controlling the way the code operates, and still others
in how the results can be interpreted and applied. In
the discussion that follows, these criteria are described
in terms of the way in which they influence the code
selection process.
5.2.1
Administrative Data
Few administrative data are, in fact, discriminatory
criteria, yet some administrative data may be indicative
of factors that exert overwhelming control over the use
of codes.  Thus, codes must be available and obtainable
if they are to be used. The pedigree of a code, while it
does not prevent the use of older versions, may imply
that newer versions should be used. Undocumented
codes would impose different emphasis on some of the
other criteria used in the evaluation. These and other
similar data will often control whether or not a code is
used at all rather than how a code is applied  to model
a given problem.
                                                   5-5

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                                                            Time Dependence
                                                          Transient/ Steady State
Figure 5-2. General Classification of Selection Criteria


                            5-6

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5.2.2      Criteria Based on Phase in the Remedial
           Process

In general,  regardless of the  nature  of the  on-site
contamination or the regulations being followed, the
remedial process for contaminated sites may generally
be divided  into three discrete phases:  the scoping
phase,  the  site  characterization  phase,  and  the
remediation phase.

The overall remedial process begins with the scoping
phase, which is designed to assess the  existing and
potential risks  that the contaminated site poses to
human health and to the environment, and to develop
site characterization plans.  The objectives of the site
characterization phase  are  to  obtain  sufficient
information to support dose and risk assessment and to
provide specific-site data required to identify feasible
remedies and remedial action goals. The final phase
of   the   remedial   process    is  the   selection,
implementation, and evaluation of a remedy. In each
phase  of the remedial process, some  information is
available to assist  in code  selection.   In  the early
stages, only broad-based decisions canbe supported by
the available data. However, as the process continues,
the available information becomes more detailed, and
the code selection can be based upon very specific
criteria dictated by the following factors:

     !      Modeling objectives
     !      Waste characteristics
     !      Hydrogeological characteristics
     !      Fate and transport processes
     !      Fluid and flow conditions
     !      Local land use and  demography

The influence that these criteria have on code selection
is fully described in Sections 3 and 4.

5.2.3      Criteria  Based  on  Waste  and  Site
           Characteristics

Section 4  presents a detailed  description of  how
specific waste and site characteristics  influence  code
selection. This section summarizes these points within
the context of completing Table 5-1.

Transport   of  radionuclides   through  subsurface
materials is influenced by the  physical and chemical
nature of both the transporting media (usually water)
and the medium through which flow occurs (usually
soil or rock). Criteria used to select or evaluate models
will be related to those processes that control the rate
of flow of water through earth materials and those
processes that either remove or deliver materials to
water as it flows through earth materials.  Subsurface
flow is controlled by two master variables, hydraulic
conductivity and driving force, and modified by the
variability or continuity among those two variables.
The hydraulic  conductivity of porous  or fractured
subsurface materials is determined by the volumetric
extent of voids or porosity within the material and the
ease or rate with which fluids can move from one void
to another.  Flow within and between void spaces is a
function of the  properties  of the  fluid and the
interaction of that fluid with the  walls of the pore
spaces.  Since most ground-water flow consists of the
movement  of dilute  water  solutions at very  low
velocity, changes in fluid properties generally can be
ignored.

The properties of the media through which the water
flows and which are of overwhelming significance in
controlling the velocity, direction, and quantity of flow
are the relative degree of saturation of the materials,
and the relative importance of fractured versus porous
media flow. These site characteristics can generally be
determined from a study of the type of soil and rock
underlying a site.

The driving force, summed up within the concept of
hydraulic head, for moving a fluid through subsurface
materials is a combination of gravity and any external
force applied to the ground-water flow system, such as
areal recharge.

The factors that control  flow through subsurface
materials can be either uniformly or non-uniformly
distributed.  When they are uniformly distributed, a
number of simplifying assumptions can be made about
the nature of flow and transport.   These simplifying
assumptions have a great influence on the application
of a mathematical model.  When subsurface material
properties are anisotropic and/or inhomogeneous, the
direction and  rate of flow will vary with position.
These site characteristics alone have a marked effect
on differentiating  among codes  which tend  to be
relatively simple and generalized and those that tend
to be relatively complex and focused.

As solutions   move   through the  spaces  within
subsurface materials, solutes may either be added to or
removed from that solution.   Which solutes are
removed or added, and the quantity and rate at which
                                                    5-7

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they are added or removed,  is  controlled by  the
geochemical  nature of the solution  and subsurface
matrix.   These geochemical process may be very
complex, and their understanding may require an
extensive base of physical and chemical data which are
rarely  available.    Because of  their  complexity,
geochemical models are generally developed as stand-
alone  modules  that  assume   equilibrium  (i.e.,
instantaneous reactions) and run independently of flow
and transport models.  The site characteristics that will
trigger  the  requirement  to  utilize  geochemical
modeling are unusual subsurface chemistry such as
sharp variations in chemical conditions  (e.g., redox,
pH) within soils and rocks.

Most subsurface transport models lump the effects of
all  geochemical reactions  into the  concept  of  the
distribution coefficient  (Kd)  or  related  retardation
factors because, without assuming  any retardation,
there would be a tendency to over-estimate the mobility
of certain highly reactive radionuclides.  There is,
however, a very wide range of experimental- and field-
determined values for distribution and retardation
coefficients, and, in practice, as with so many other
characteristics,  these parameters are  usually best
determined on a site-specific basis. At many sites, it
may be unknown whether predicted changes in  the
concentration of radionuclides in ground water can be
adequately  explained by the simplifying  assumptions
that underlay the Kd concept.  As the assumption of a
Kd   to   calculate   radionuclide  partitioning   is
theoretically valid only if:  (1) chemical equilibrium
exists among all aqueous species containing the solute;
(2) reversible, linear sorption is the dominant process
controlling  exchange  of the  solute between  the
groundwater and the  rock; and (3)  transport of the
solute by particulates  (colloids) is insignificant.  The
site characterization program would need to determine
if  these  assumptions are  valid for radioelement
transport in the ground water or if deviations from
these conditions  will produce   significant  errors.
Consequently,  focused  geochemical modeling  and
laboratory  studies  may be  needed to address these
uncertainties.

The  conceptual model is the set  of  hypotheses  and
assumptions about the physical characteristics (e.g.,
aquifer  properties  and  boundary   type)  and  the
phenomena (e.g., model of fluid flow) that describes
and postulates the behavior of the actual system. The
approach to  formulating an appropriate conceptual
model(s) of the  site  integrates the  generalized
knowledge of physical processes with the  available
information.  Therefore, a conceptual model provides
a simplifying framework in which information can be
organized  and  linked  to  processes  that  can be
simulated with predictive models.

The   mathematical  model  is   the   mathematical
representation  of  the  conceptual   model.     A
mathematical model might include coupled algebraic,
ordinary or partial differential, or integral equations
that approximate the physical processes for a specified
portion of the site conceptual model.  The process by
which the input and output of various mathematical
models may be linked to support the conceptual model
in order to meet the modeling objectives also plays an
important role in the selection of a computer code(s).
For example, the conceptual model may include flow
and transport processes in both the unsaturated and
saturated zones, in which case it would be possible to
select  one  code that  would simulate the flow  and
transport processes in the unsaturated zone at the
desired level  of detail  and to use this model output as
input into a second code which is capable of simulating
flow  and  transport  within  the saturated  zone.
Therefore,  the code selection and evaluation process
has to reflect  this availability to potentially dissect the
conceptual model into discrete  components.

The   overall  application  of this  approach  will
essentially be reduced to two considerations:  (1) each
component of the  conceptual model is adequately
described by the mathematical model; and (2) each of
the   separate  mathematical   models  has  been
successfully integrated to where the sum of the parts is
equal to the whole.  The second consideration is more
applicable to the application of the code and will be far
more difficult to evaluate than the first.
Each code, however, should  individually  meet the
basic  criteria which  are  related   to   the   site
characteristics  and which have been outlined as
general components of the conceptual model that need
to be considered when assessing the appropriateness of
a computer code (Figure 5-3).
                                                   5-8

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                                                SITE RELATED
 Source-Term
Characteristics
Aquifer-System
Characteristics
Transport and
 Fate Process
Flow Conditions
  Time Dependence
Transient/Steady State
                           What site-related characteristics are described by the code?
             Are the physical characteristics described by the code consistent with the conceptual model?
           Do assumptions and limitations that are Inherent within the code provide cause for code rejection?
                  Figure 5-3.  Physical, Chemical, and Temporal Site-Related Selection Criteria


                                                         5-9

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These broad subjects are  further broken down into
their individual components both in the table presented
as Appendix D  and in the discussion presented in
Sections 3 and 4.
5.2.4
Criteria Based on Code Characteristics
A contaminant fate and transport model results from
the application  of  a previously  written or  new
computer code to a specific problem via the collection
of input  data and  the parameterization  of site
characteristics. The  resultant model is, therefore, a
merger of  a mathematical  formulation,  solution
methodology, data, and ancillary information which
enhances or controls the use of the model. Therefore,
in addition to selection criteria  for the  modeling
objectives which  were presented in  the  previous
section, the code evaluation process must also consider
attributes that are integral components of the computer
code(s) including:

           Source Code Availability
           History of Use
           Code Documentation
           Code Testing
           Hardware Requirements
           Code Output
           Solution Methodology
           Code Dimensionality

The development of selection criteria presented in this
section takes an approach  consistent with industry
standards by relying on published reports pertaining to
the quality assurance and  quality  control  in the
development and application of computer codes.

Source Code Availability

To facilitate a thorough review of the generic code,
detailed  documentation  of  the   code   and  its
developmental history is required.  Also, the source
code must be available for inspection (Figure 5-4). In
addition, to ensure  independent  evaluation  of the
reproducibility  of the verification  and validation
results, the computer  source code  as well  as the
compiled version of the code  (i.e.,  computer code in
machine language) should be  available for use by the
reviewer, together with files  containing the original
test data used in the code's verification and validation.
History of Use

Much of the information needed for a thorough code
evaluation can  be  obtained  from  the author  or
distributor of the code (Figure 5-4).  In fact, inability
to obtain the  necessary  publications  can  be  an
indication that the code is either not well documented
or that the code is not widely used. In either case, the
inaccessibility  of  the  documentation  and  related
publications should be strong grounds for deciding that
the code is unacceptable.

The acceptance and evaluation process should rely on
user opinions and published information in addition to
hands-on experience and testing.  User opinions are
especially valuable in determining whether the code
functions as documented or has significant errors or
shortcomings. In some instances, users independent of
the  developer have performed extensive testing and
bench-marking or are familiar with published papers
documenting the use of the code. Users will also have
first-hand knowledge about how easy it is to use the
code and what level of experience  is required.

Quality Assurance

It is recommended  that code  selection criteria  be
closely tied to the quality assurance criteria which were
folio wed during the development of the computer code.
These criteria will be associated with the adequacy of
the code testing and documentation (Figure 5-5).

Quality assurance in modeling is the procedural and
operational framework put in place by the organization
managing the modeling study, to assure technically
and scientifically adequate execution of all  project
tasks included in  the study,  and to assure that  all
modeling-based analysis is verifiable and defensible
(TAY85).

The  two  major elements of quality assurance  are
quality control and quality assessment. Quality control
refers to the procedures that ensure the quality of the
final product.  These  procedures include  the  use  of
appropriate methodology in
                                                  5-10

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                                                   CODE  RELATED
                         Source Code
                          Availability
Public Domain
Commercially
  Available
Project Specific
        Is source code available for independent review?
       Is executable code available for Independent review?
                                                          History of Use
                             Figure 5-4.  Source Code Availability and History of Use Selection Criteria


                                                            5-11
                                                                                                             Is code user friendly?
                                                                                                             Has code been used
                                                                                                             on similar problems?
                                                                                  Have previous users
                                                                                   been surveyed?
                                                                                 Are published reports
                                                                                      available?
                                                                                                              Are code authors
                                                                                                          available for consultation?

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                                                            CODE RELATED
                                                           Quality Assurance
 Adequacy of
Documentation
                Code Development
                     Report
                           Adequacy of
                              Testing
                                                                                                          _L
                                           Is report properly
                                             documented?
Verification
                                           Is verification process
                                          adequately described?
Field Testing
                                                                                  Was testing against
                                                                                  problems of similar
                                                                                 complexity completed?
                                     Extended model description
                                     Model Input data description and format
                                     Type of output data provided
                                     Code execution preparation Instructions
                                     Sample model runs
                                     Trouble shooting guide
                                     Functional description of the model
                                     Model input and output data
                                     Code verification and validation Information
      Model specifications
      Model description
      Flow charts
      Descriptions of routines
      Database description
      Source listing
      Error messages
                                            Were any fie Id
                                           tests performed?
                                                                                                                    Over what scales?
                                        Over what time frame?
                                                                                                                  Which processes have
                                                                                                                     been validated?
                                          Figure 5-5. Quality Assurance Selection Criteria

                                                                 5-12

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developing and applying computer simulation codes,
adequate verification and validation procedures, and
proper usage  of the  selected  methods  and codes
(HEI92).  To monitor the quality control procedures
and to evaluate the quality of the studies, quality
assessment is applied (HEI89).

Software quality assurance  (SQA)  consists  of the
application  of procedures,  techniques,  and tools
through the software  life cycle, to ensure that the
products  conform  to  pre-specified  requirements
(BRY87). This requires that in the initial stage of the
software  development  project,  appropriate  SQA
procedures (e.g., auditing,  design inspection, code
inspection, error-prone analysis, functional testing,
logical testing, path testing, reviewing, walk-through),
and tools (e.g., text-editors, software debuggers, source
code comparitors, language  processors) need to be
identified  and  the  software  design  criteria  be
determined (HEI92).

Quality   assurance   for  code  development  and
maintenance implies a systematic approach, starting
with the careful formulation of code design objectives,
criteria and standards,  followed by an implementation
strategy.  The implementation strategy includes the
design of the code structure and a description of the
way in which software engineering principles will be
applied to the code.  In this planning stage, measures
are to be taken to ensure complete documentation of
code design and implementation, record keeping of the
coding  process,  description of  the purpose  and
structure   of   each  code   segment   (functions,
subroutines),  and  record-keeping  of  the  code
verification process.

Records for the coding and verification process may
include:  a description of the fundamental algorithms
describing the physical process(es) which are to be
modeled;  the  means  by  which  the mathematical
algorithms have been translated into computer code
(e.g.,  Fortran);  results of  discrete checks on the
subroutines for accuracy; and comparisons among the
codes' numerical solutions with either analytical or
other independently verified numerical solutions.

Code verification or testing ensures that the underlying
mathematical   algorithms   have  been   correctly
translated  into  computer code.   The  verification
process  varies for different codes and ranges from
simply checking the results of a plotting routine to
comparing the results of the computer code to known
analytical solutions or to results from other verified
codes.

Traceability describes the  ability  of the  computer
analyst to identify the software which was used to
perform a particular calculation, including its name,
date, and version number, while retrievability refers to
the availability of the same version of the software for
further use.

Code Documentation

Detailed   guidelines   for   the  preparation  of
comprehensive software documentation are given by
the Federal Computer Performance Evaluation and
Simulation  Center  (FED81).    This  publication
discusses the structure recommended for four types of
manuals providing model information for managers,
users,  analysts and programmers.   According to
FEDSIM  (1981), the manager's summary manual
should   contain   a  model   description,   model
development history, an experimentation report, and a
discussion of current  and  future    applications.
Currently, ASTM (American Society for Testing and
Materials) is developing a standard ground-water code
description for this specific purpose (HEI92).

As discussed in van der Heijde  (1992),  the code
documentation should include  a description  of the
theoretical framework represented by the generic
model on which the code is based, code structure and
language standards applied, and code use instructions
regarding model setup and code execution parameters.
Furthermore, the documentation should also include a
complete treatment of the  equations  on which the
generic model is based, the underlying mathematical
and conceptual assumptions, the boundary conditions
that are incorporated  in the model, the method and
algorithms used  to solve  the  equations,  and the
limiting   conditions  resulting  from  the  chosen
approach.  The documentation should also include
user's instructions for implementing and operating the
code, and preparing data files.  It should present
examples of model formulation (e.g., grid design,
assignment of boundary conditions), complete with
input and output file descriptions and include an
extensive  code verification and validation or field
testing  report.     Finally,  programmer-orientated
documentation should provide instructions for code
modification and maintenance.
                                                  5-13

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An integral part of the code development process is the
preparation  of  the  code  documentation.   This
documentation of QA in model development consists
of reports and files pertaining to the development of
the model and should include (HEI92):

          A report on the development of the code
          including the (standardized and approved)
          programmer's bound notebook containing
          detailed   descriptions  of   the   code
          verification process;

          Verification report including verification
          scenarios, parameter values, boundary and
          initial conditions, source-term conditions,
          dominant flow  and transport processes;

          Orientation and spacing of the  grid and
          justification;

          Time-stepping  scheme and justification;

          Changes and documentation of changes
          made in code after baselining;

          Executable and source code  version  of
          baselined code;

          Input   and   output   (numerical   and
          graphical)  for each verification run;

          Notebook  containing reference  material
          (e.g., published papers, laboratory results,
          programmers rationale) used to formulate
          the verification problem.

Furthermore, the software should be documented in
sufficient detail to (GAS79):

          record technical information that enables
          system and program changes to  be made
          quickly and effectively;

          enable programmers and system analysts,
          other than  software originators, to use and
          to work on the  programs;

          assist the user  in understanding  what the
          program is about and what it can do;

          increase program sharing potential;
          facilitate  auditing and verification  of
          program operations;

          provide  managers with information  to
          review   at   significant  developmental
          milestones so that they may independently
          determine that project requirements have
          been met  and  that  resources  should
          continue to be expended;

          reduce  disruptive  effects  of  personnel
          turnover;

          facilitate understanding among managers,
          developers,  programmers, operators, and
          users by providing  information about
          maintenance, training, and changes in and
          operation of the software;

          inform   other  potential  users  of the
          functions and capabilities of the software,
          so  that they  can determine whether it
          serves their needs.

The user's manual should, at a minimum, consist of:

          an extended code description;

          code input data description and format;

          type of output data provided;

          code execution preparation instructions;

          sample model runs;

          trouble shooting guide; and

          contact person/affiliated office.

The  programmer's manual should, at a minimum,
include:

          code specifications;
          code description;
    •     flow charts;
          descriptions of routines;
          data-base description;
          source listing;
          error messages; and
          contact person/affiliated office.
                                                  5-14

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The analyst's manual should, at a minimum, present:

           a functional description of the code;

           code input and output data;
           code   verification   and   validation
           information; and

           contact person/affiliated office.

The code itself should be well structured and internally
well documented; where possible,  self-explanatory
parameter, variable, subroutine, and function names
should be used.

Code Testing

Before a code can be used as a planning and decision-
making  tool,  its  credentials  must  be established
through systematic testing of the code's correctness and
evaluation of the code's performance  characteristics
(HEI89). Of the two major approaches available, the
evaluation or review process is rather qualitative  in
nature, while code-testing  results can be expressed
using quantitative performance measures.

Code testing  (or code verification)  is  aimed  at
detecting programming errors,  testing  embedded
algorithms,  and   evaluating   the  operational
characteristics of the  code  through its execution on
carefully selected example test problems and test data
sets. ASTM84 defines verification as the examination
of the numerical technique in the computer code  to
ascertain that it truly represents the conceptual model,
and that there are no inherent problems with obtaining
a correct solution.

At this point, it is necessary to point out the distinction
between  generic   simulation  codes   based on an
analytical  solution  of  the governing equation(s)
(Appendix C) and codes that include a numerical
solution. Verification of a coded analytical solution is
restricted to comparison with independently calculated
results using the same mathematical expression, i.e.,
manual calculations, using the results from computer
programs  coded  independently  by  third  party
programmers. Verification  of a code formulated with
numerical  methods   might take  two  forms: (1)
comparison with  analytical solutions, and  (2) code
intercomparison between numerically based codes,
representing the same generic simulation model, using
synthetic data sets.
It is important to distinguish between code testing and
model testing. Code testing is limited to establishing
the correctness  of the  computer code with respect to
the criteria and  requirements for which it is designed
(e.g.,  to represent the  mathematical model).  Model
testing (or model validation) is more  inclusive than
code  testing,  as it  represents the  final  step  in
determining  the   validity   of  the   quantitative
relationships  derived  for the real-world system  the
model is designed to simulate.

Attempts to validate models must address the issue of
spatial  and temporal variability when comparing
model predictions with limited field observations.  If
sufficient  field  data  are obtained  to derive  the
probability distribution of contaminant concentrations,
the results of a stochastic model can be compared
directly.  For a deterministic  model, however,  the
traditional approach has been to vary  the input data
within its expected range of variability (or uncertainty)
and determine whether the model results satisfactorily
match historical field  measured values. This code-
testing exercise is sometimes  referred to as history
matching.

Konikow   and   Bredehoeft  (KON92) present  a
compelling argument that computer models cannot be
truly  validated  but can only  be  invalidated.   As
reported by Hawking (HAW88), any physical theory is
only  provisional, in  the sense that  it is  only a
hypothesis that  can never be proven. No matter how
many times the  results of the experiments agree with
some theory, there is never complete certainty that the
next test will not contradict the theory. On the other
hand, a theory  can be disproven by finding even a
single observation that disagrees with the predictions
of the theory.

From a philosophical perspective, it  is difficult to
develop selection  criteria  for a model validation
process  which may be  intrinsically flawed. However,
the average strategy presented in this chapter provides
some  assurance that the code selected has the highest
probability of  most  accurately  representing  the
conceptual model.
                                                  5-15

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Hardware Requirements

In general, hardware requirements should rarely be a
discriminatory factor in the selection of a computer
code (Figure 5-6). However, a number of the available
codes require very sophisticated hardware, not so much
because of the intrinsic requirements of the code but
because the simulated processes may be very complex
and  require  time-consuming  solution  methods.
Therefore, hardware requirements should be  clearly
identified for the code itself and be consistent with the
hardware available to the user.

Mathematical Solution Methodology

Every ground-water or contaminant transport model is
based upon a set of mathematical equations. Solution
methodology refers to the strategy and techniques used
to solve these equations.  In ground-water modeling,
the equations  are normally solved  for head (water
elevations  in  the  subsurface)  and/or contaminant
concentrations.

Mathematical  methods can be broadly classified as
either  deterministic  or  stochastic  (Figure  5-7).
Deterministic methods assume that a system or process
operates such  that the  occurrence of a given set of
events   leads  to a uniquely  definable  outcome.
Stochastic methods pre-suppose the outcome to be
uncertain and  are  structured to account for  this
uncertainty.

Most stochastic methods are not completely stochastic
in that they often utilize a deterministic representation
of soil processes and derive their stochastic nature
from their representation  of  inputs  and/or  spatial
variation of soil characteristics and resulting chemical
movement (i.e., Monte Carlo). While the deterministic
approach results in a specific value of a soil variable
(e.g., solute concentration) at pre-specified points in
the domain, the stochastic approach provides the
probability (within a level of confidence) of a specific
value occurring at any point.

Deterministic methods may be broadly classified as
either analytical or numerical.   Analytical methods
usually  involve approximate or  exact solutions to
simplified forms of the differential equations for water
movement and solute transport.  Simple  analytical
methods are based  on the solution  of applicable
differential  equations  which  make  a simplified
idealization of the field and give qualitative estimates
of the extent of contaminant transport.  Such models
are  simpler to use than numerical models and can
generally  be solved with  the  aid of a calculator,
although computers are also used.  Analytical models
are  restricted  to simplified  representations  of the
physical situations and generally require only limited
site-specific input data. They are useful for screening
sites and scoping the problem to determine data needs
or the applicability of more detailed numerical models.

Analytical  solutions  are   used  in   modeling
investigations  to  solve  many  different kinds  of
problems.   For  example,  aquifer parameters are
obtained from  aquifer pumping and  tracer  tests
through the use of analytical models, and ground-water
flow and  contaminant transport rates can also  be
estimated with the use of analytical models.

Numerical models provide solutions to the differential
equations  describing  water  movement  and  solute
transport  using  numerical  methods such as  finite
differences and finite elements.  Numerical methods
account for complex  geometry and  heterogenous
media, as well as dispersion, diffusion, and chemical
retardation processes (e.g.,  sorption, precipitation,
radioactive decay, ion exchange, degradation). These
methods almost always require a digital computer,
greater quantities of data than analytical modeling, and
experienced modelers.

The validity of the results from mathematical models
depends strongly on the quality and quantity of the
input data. Stochastic, numerical, and analytical codes
have strengths and weaknesses inherent within their
formulations, all of which need to be considered prior
to their selection.

Code Output

One aspect of the computer  code that is frequently
ignored in the selection process is the  form of the
model output (Figure 5-8).  It is true, however, that in
most instances the actual output can be fashioned into
the  desired format,  provided  the model itself is
consistent with required output (e.g., output in three
dimensions cannot be obtained with a two-dimensional
model).
                                                   5-16

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Micro/ PC Based
                                 CODE RELATED
                              Hardware Requirements
Mini/Workstation
     Based
                                Memory Requirements
                                  Operating System
                                  (e.g., UNIX, DOS)
Supercomputer
                   Figure 5-6. Hardware Requirements Selection Criteria


                                       5-17

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                                       CODE RELATED
                                       Mathematical
                                   Solution Methodology
         Deterministic
Analytical
                                               Stochastic
                           1
Numerical
Monte Carlo
Moment Analysis
                 Are overall solution techniques appropriate for specific problems?
                         Are numerical efficiency and stability achieved?
                                 Is mass balance maintained?
                    Figure 5-7.  Mathematical Solution Methodology Acceptance Criteria

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CODE RELATED


Code Output

Contaminant Concentration
as a Function of Distance
from Surface

Contaminant Plume

Specified Source Rate

Mass Balance

Error Messages

Matrix Formulation Type Information














Combined Cumulative Distribution
Functions of Release Probability

Dose and/or Concentration

Breakthrough Curves at Selected
Points Over Time

As an Average or as Discrete Values
at Selected Points or Cells

Continuously Distributed in
Space

As a Function of Depth from
Surface
Figure 5-8. Code Output Selection Criteria




                 5-19

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In general, the model output is expressed in terms of
hydraulic   head,   pressure,  velocities,  or  solute
concentrations.  The spatial  coverage  of parameter
output values is either dependent on the frequency of
nodal spacing (numerical) or on the number  of
specified x and y coordinates (analytical) which are
included in the model input files.  Model output will
also vary due to the inherent nature of the code itself.
For example,  codes  that simulate  movement in the
unsaturated zone generally produce saturationprofiles.
These profiles indicate the percentage of the pore space
that is filled with water, whereas saturated zone codes
have no need forthis capability because all of the pores
below  the water  table  are  assumed  to  be filled
completely with water.  The single most important
code selection criteria, relative to the model output,
would  be that  the  code  provides mass-balance
information. A mass-balance determination is a check
to ensure  that the amount  of water  or contaminant
mass entering the system equals the amount exiting the
system plus the change in the quantity stored in the
system.  If there  is a significant discrepancy in the
model's mass balance, something may be wrong with
the numerical solution,  although errors in the mass
balance may  also indicate  problems with the mass-
balance formulation  itself.  Therefore, mass-balance
information not  only  provides  a  check  on  the
mathematical formulations  within the code, but also
assists in  ensuring that input parameter conversions
and  other errors have  not been made.  It is  not
uncommon for codes that  do include mass-balance
output to provide  information (e.g., fluxes, heads) on
specific boundaries as well  as the source term, all of
which can be used in  the interpretation and evaluation
of the predicted flow and solute transport directions
and rates.

Code Dimensionality

The determination as  to the number of dimensions that
a  code  should be capable of  simulating is based
primarily  upon  the  modeling  objectives  and  the
dimensionality of the processes the code is designed to
simulate (Figure 5-9).

In determining how many dimensions are necessary to
meet the objectives,  it becomes necessary to gain a
basic understanding  of  how  the physical  processes
(e.g., ground-water flow and transport) are affected by
the exclusion or inclusion of an additional dimension.
It should be kept in mind that the movement of ground
water and contaminants is  usually controlled by
advective   and  dispersive  processes  which  are
inherently  three-dimensional.   Advection is  more
responsible for the length of time (i.e., travel time) it
takes for a contaminant to travel from the source term
to a downgradient receptor, while dispersion directly
influences the concentration of the contaminant along
its travel path.  This fact is very important in that it
provides an intuitive sense forthe effect dimensionality
has   on   contaminant   migration   rates   and
concentrations.

As a general rule, the fewer the dimensions, the more
the model results will over-estimate concentrations and
under-estimate travel times. In a model with fewer
dimensions, predicted concentrations will generally be
greater  because   dispersion,  which   is  a  three-
dimensional process, will be dimension limited and
will not occur to the same degree as it actually would
in the field. Similarly, predicted travel times will be
shorter than the actual travel time, not because of a
change  in the  contaminant velocities but because a
more direct travel path is assumed.  Therefore, the
lower  dimensionality  models  tend  to  be  more
conservative in their predictions and are frequently
used for screening analyses.

One-dimensional simulations of contaminant transport
usually   ignore   dispersion  altogether,   and
contamination  is  assumed to  migrate solely  by
advection, which may result in a highly conservative
approximation. Vertical analyses in one dimension are
generally reserved for evaluating flow and transport in
the unsaturated zone. Two-dimensional analyses of an
aquifer  flow system can be performed as either a
planar representation, where flow and transport are
assumed to be  horizontal (i.e., longitudinal and
transverse components), or as a cross  section where
flow and transport components are confined to vertical
and horizontal components.

In most instances,  two-dimensional   analyses  are
performed in an areal orientation, with the exception
of the  unsaturated  zone,  and  are based  on  the
assumption that most contaminants enter the saturated
system from above and that little vertical dispersion
occurs.  However, a number of limitations accompany
two-dimensional planar simulations. These include
the inability to simulate multiple layers (e.g., aquifers
and  aquitards) as well as any partial penetration
effects.  Furthermore,  because vertical
                                                  5-20

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CODE RELATED
Dimensionality
                         Have critical dimensions of the
                          dominant physical processes
                                been identified?
                    Is code capable of simulating the identified
                          processes in required number
                                of dimensions?
         Figure 5-9.  Code Dimensionality Selection Criteria


                         5-21

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components of flow are ignored,  an artificial lower
boundary   on  contaminant  migration  has  been
automatically assumed which may or may not be the
case.

A two-dimensional formulation of the flow system is
frequently  sufficient for  the  purposes  of  risk
assessment provided that flow and transport in the
contaminated aquifer are essentially horizontal.  The
added complexities of a  site-wide, three-dimensional
flow and transport simulation are often believed  to
outweigh the expected improvement in the evaluation
of risk.    Complexities  include  limited  site-wide
hydraulic  head and  lithologic data with depth and
significantly increased computational demands.

Quasi-three-dimensional analyses remove some of the
limitations inherent in two-dimensional  analyses.
Most notably,  quasi-three-dimensional  simulations
allowforthe incorporation of multiple layers; however,
flow and transport in the aquifers are still restrained to
longitudinal and transverse horizontal components,
whereas flow and transport in the  aquitards are even
further restricted to  vertical flow components only.
Although  partial penetration  effects still cannot be
accommodated in quasi-three-dimensional analyses,
this  method   can   sometimes   provide  a  good
compromise between the  relatively  simplistic two-
dimensional analysis and the complex,  fully three-
dimensional analysis. This is  the case, particularly if
vertical movement of contaminants or recharge from
the shallow aquifer through a  confining unit and into
a deeper aquifer is suspected.

Fully three-dimensional modeling generally allows
both the geology  and all of the dominant flow and
transport   processes  to  be  described  in  three
dimensions. This approach usually affords the most
reliable means  of predicting ground-water flow and
contaminant transport characteristics, provided that
sufficient representative data are available for the site.

Although  the  intrinsic dimensionality  of the code
should be an important consideration relative to the
acceptance or rejection of the code, this determination
will also be closely tied to the code  application and
modeling objectives.
                                                  5-22

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                                         REFERENCES
AND92     Anderson, M.P., and W.W. Woessner, 1992.  Applied Groundwater Modeling:  Simulation of Flow
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ASTM84    Am. Soc. for Testing and Materials (ASTM), 1984.  Standard Practices for Evaluating
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BAE83      Baes, C.F., and R.D. Sharp, 1983.  "A Proposal for Estimation of Soil Leaching Constants for Use in
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BAC80      Bachmat, Y., J. Bredehoeft, B. Andrews, D. Holtz, and S. Sebastian, 1980. Ground-Water
            Management:  The use of numerical models, Water Resources Monograph 5. American Geophysical
            Union, Washington, D.C., 127 pp.

BRY87      Bryant, J.L., and N.P. Wilburn, 1987. Handbook of Software Quality Assurance Techniques
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            Nuclear Regulatory Commission, Washington, D.C.

DOE91      Department of Energy, 1991.  Ground-Water Model Development Plan in Support of Risk
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EPA88      Environmental Protection Agency, 1988.  "Guidance for Conducting Remedial Investigations and
            Feasibility Studies Under CERCLA," EPA/540/G-89/004, OSWER Directive 9355.3-01, October
            1988.

EPA90      Environmental Protection Agency, OSWER, 1990. OSWER Models Management Initiative:  report
            on the usage of computer models in hazardous waste/superfund programs. Phase II Final Report.
            December 1990.

EPA91      Environmental Protection Agency, 1991.  Integrated Model Evaluation System (TMESX prepared for
            Office of Health and Environmental Assessment, Exposure Assessment Group, Washington, D.C.

EPA93      Environmental Protection Agency, "Environmental Pathway Models - Ground-Water Modeling in
            Support of Remedial Decision Making at Sites Contaminated with Radioactive Material," EPA 402-
            R-93-009, March 1993.

FED81      Federal Computer Performance Evaluation and Simulation Center (FEDSIM), 1981. Computer
            Model Documentation Guide. NBS Special Publ. 500-73, Inst. for Computer Science and
            Technology, Nat. Bur. of Standards, U.S. Dept. of Commerce, Washington, D.C.

GAS79      Gass, S.I., 1979.  Computer Model Documentation:  A Review and an Approach. NBS Special Publ.
            500-39, Inst. for Computer Science and Technology, Nat. Bur. of Standards, U.S. Dept. of
            Commerce, Washington, D.C.

GIL88      Gilbert, T.L., M.J. Jusko, K.F. Eckerman, W.R. Hansen, W.E. Kennedy, Jr., B.A. Napier, and
            J.K. Soldat. "A Manual for Implementing Residual Radioactive Material Guidelines" (RES-RAD),
            U.S. Department of Energy, 1988, 217 pp.
                                               Ref-1

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GRA6-1     Environmental Protection Agency, 1992.  Ground-Water Modeling Compendium, EPA/540/G-
            88/003.

GRA6-1     Environmental Protection Agency. Basics of Pump and Treat Ground-Water Remediation
            Technology, EPA/600/9-90/003.

GRA6-1     Environmental Protection Agency, 1988.  Guidance on Remedial Actions for Contaminated Ground
            Water at Superfund Sites, EPA/540/G-88/003.

GRA6-1     EPA, 1988.  Superfund Exposure Assessment Manual, EPA/540/1-88/001.

HAW88     Hawking, S.W., 1988.  A Brief History of Time: From the Big Bank to Black Holes.  Bantam Books,
            New York, 1988.

HEI92       van der Heijde, P.K.M., and O.A. Elnawawy, 1992. Compilation of Ground-water Models. GWMI
            91-06.  International Ground Water Modeling Center, Colorado School of Mines, Golden, Colorado.

HEI89       van der Heijde, P.K.M., 1989. Quality Assurance and Quality Control in Groundwater Modeling.
            GWMI 89-04. Internal. Ground Water Modeling Center, Holcomb Research Inst, Indianapolis,
            Indiana.

HEI88       van der Heijde, P.K.M., and M.S. Beljin, 1988.  Model Assessment for Delineating Wellhead
            Protection Areas. EPA 440/6-88-002, Office of Ground-Water Protection, U.S. Environmental
            Protection Agency, Washington, D.C.

HUY91      Huyakorn, P.S., J.B.  Kool and Y.S. Wu, October 1991. VAM2D - Variability Saturated Analysis
            Model in Two Dimensions. Version 5.2 with Hysteresis and Chain Decay Transport.  NUREG/CR-
            5352, Rev. 1. U.S. Nuclear Regulatory Commission, Washington, D.C.

KON78      Konikow, L., and J. Bredehoeft,  1978. Computer model of two-dimensional solute transport and
            dispersion in ground water. U. S. Geological Survey Water Resources Investigation, Book 7, Chapter
            C2.

KON92      Konikow, L.F., and J.D. Bredehoeft,  1992. Ground-Water Models Cannot be Validated.  Advances
            in Water Resources SWRENI 15(1): 75-83.

MCD88     McDonald, M.G., and A.W. Harbaugh, 1988. A Modular Three-Dimensional Finite-Difference
            Ground-Water Flow Model. U. S. Geological Survey TWRI, Book 6, Chapter Al.

MER81      Mercer, J.W., and C.R. Faust, 1981.  Ground Water Modeling, Nat. Water Well Assoc., Dublin,
            Ohio.

MOS92      Moskowitz, P., R. Pardi, M. DePhillips, and A.  Meinhold, 1992.  Computer models used to support
            cleanup decision making at hazardous waste sites. Brookhaven National Laboratory.

NRC86      Nuclear Regulatory Commission, 1986. "Update of Part 61 Impacts Analysis Methodology,"
            Prepared by O.I. Oztunali, W.D. Pon, R. Eng, and G.W. Roles, NUREG/CR-4370, January 1986.

NRC90      Nuclear Regulatory Commission, 1990. "Background Information for the Development of a Low-
            Level Waste Performance Assessment Methodology.  Computer Code Implementation and
            Assessment," Prepared by Sandia National Laboratory, NUREG/CR-5453, August 1990.
                                               Ref-2

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NRC90a    Nuclear Regulatory Commission, 1990. "Performance Assessment Methodologies for Low-Level
            Waste Facilities," Prepared by Sandia National Laboratory, NUREG/CR-5532, July 1990.

PAR92      Pardi, R.R., Daum, M.L., and Moskowitz, P.O., 1992. Environmental Characteristics of EPA. NRC.
            and DOE Sites Contaminated with Radioactive Substances.  U. S. Environmental Protection Agency,
            Office of Radiation Programs, Washington, D.C.

SHE90      Sheppard, M.I., and E.L. Gershey, 1990. "Default Solid Soil/Liquid Partition Coefficients, Kds, for
            Four Major Soil Types: A Compendium," Health Physics. 59 (4):471, October 1990.

TAY85      Taylor, J.K., 1985.  What is Quality Assurance?  In:  J.K. Taylor and T.W. Stanley (eds.), Quality
            Assurance for Environmental Measurements, pp. 5-11. ASTM Special Technical Publication 867,
            Am. Soc. for Testing and Materials, Philadelphia, Pennsylvania.

ZHE90      Zheng, C., 1990.  A Modular Three-Dimensional Transport Model for Simulation of Advection,
            Dispersion, and Chemical Reactions of Contaminants in Ground-Water Systems, Prepared for the
            United States Environmental Protection Agency, Robert S. Kerr Environmental Research Laboratory,
            Ada, Oklahoma.
                                                Ref-3

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                                        BIBLIOGRAPHY
Barney, G.S., J.D. Navratil, and W.W. Schultz, 1984.  Geochemical Behavior of Disposed Radioactive Waste.
American Chemical Society, Washington, D.C.

Bear, J., 1979.  Hydraulics of Ground Water. McGraw-Hill Book Company.

Boonstra, J. and N.A. de Ridder, 1981.  Numerical Modeling of Ground-Water Basins. ILRI Publication 29.

de Marsily, G., 1986. Quantitative Hydrogeology. Ground-Water Hydrology for Engineers, Academic Press, Inc.

Drever, J.I., 1982. The Geochemistry of Natural Waters. Prentice-Hall Inc., Englewood Cliffs, N.J.

Environmental Protection Agency, 1985. "Modeling Remedial Actions at Uncontrolled Hazardous Waste Sites,"
EPA/540/2-85/001, Office of Solid Waste and Emergency Response and Office of Research and Development.

Environmental Protection Agency, 1987. "The Use of Models in Managing Ground-Water Protection Programs,"
EPA/600/8-87/003, Robert S. Kerr Environmental Research Laboratory.

Environmental Protection Agency, 1988. "Groundwater Modeling: An Overview and Status Report," EPA/600/2-
89/028, Robert S. Kerr Environmental Research Laboratory.

Environmental Protection Agency, 1989.  "Predicting Subsurface Contaminant Transport and Transformation:
Considerations for Model Selection and Field Validation," EPA/600/2-89/045, Robert S. Kerr Environmental
Research Laboratory.

Environmental Protection Agency, 1992. "Quality Assurance and Quality Control in the Development and
Application of Ground-Water Models," EPA/600/R-93/011, Office of Research and Development.

Environmental Protection Agency, 1992. "Ground-water Modeling Compendium," EPA-500-B-92-006, Office of
Solid Waste and Emergency Response.

Environmental Protection Agency, 1993. "Compilation of Ground-Water Models," EPA/600/R-93/118, Office of
Research and Development.

Fetter,  C.W., 1993.  Contaminant Hydrogeology. Macmillan Publishing Company.

Freeze, R.A.  and J.A. Cherry, 1979. Ground Water. Prentice-Hall, Inc.

Hern, S.C. and S.M. Melancon, 1986.  Vadose Zone Modeling of Organic Pollutants.  Lewis Publishers, Inc.
Chelsea, Michigan.

Istok, J., 1989. Ground-Water Modeling by the Finite Element Method. Water Resources Monograph 13,
American Geophysical Union.

Jorgensen, S.E., 1984. Modelling the Fate and Effect of Toxic Substances in the Environment. Developments in
Environmental Modelling, 6.

Jury, W.A., W.R. Gardner and W.H. Gardner, 1991.  Soil Physics. Fifth Edition. John Wiley & Sons, Inc.
                                                Bib-1

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Liggett, J.A., and P.L-F. Liu, 1983. The Boundary Integral Equation Method for Porous Media Flow. School of
Civil and Environmental Engineering, Cornell University, N.Y.

Matthess G., 1982. The Properties of Ground Water. John Wiley & Sons, Inc.

Resources Management and Information Staff, 1992. Ground-Water Modeling Compendium OSWER Models
Management Initiative: Pilot Project on Ground-Water Modeling.  Office of Solid Waste and Emergency
Response.

Thomas, R.G., 1973.  "Groundwater Models," Food and Agriculture Organization of the United Nations, Rome,
FAO Irrigation and Drainage Paper.

Wang, H.F. andM.P. Anderson, 1982.  Introduction to Ground-Water Modeling. Finite Difference and Finite
Element Methods.  W.H. Freeman and Company.
                                               Bib-2

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APPENDIX A
 GLOSSARY
    A-l

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                                            GLOSSARY
ACTINIDES - Elements 90 through 103.

ADSORPTION - Physical attraction and adhesion of gas, vapor, or dissolved molecules to the surface of solids
without chemical reaction.

ADVECTION - The process by which solutes are transported by the bulk motion of flowing ground water.

ALLUVIAL FLOODPLAIN - The lowland adjacent to a river, usually dry but subject to flooding when the river
overflows its banks.  It is that flat area constructed by the present river in the present climate. It is built of
alluvium carried by the river during floods and deposited in the sluggish water beyond the influence of the swiftest
current.

ANALYTICAL MODEL - A model based on known initial and boundary conditions which incorporates a
continuous exact solution of a simple flow or solute transport equation such as Darcy's Law.  Analytical models are
ordinarily restricted to conditions of homogeneous, isotropic flow, and transport.

ANION EXCLUSION - Negatively charged rock surfaces can affect the movement of anions, by either retarding
the movement of anions by not allowing negatively charged radionuclides to pass through the pore opening or by
enhancing the transport of ions by restricting the anion movement to the center of the pore channel where ground-
water velocities are higher.

ANISOTROPIC - Having some physical property that varies with direction of flow.

AQUIFER - A unit of porous material capable of storing and transmitting appreciable quantities of water to wells.

AQUITARD - A saturated, but poorly permeable bed, formation, or group of formations that can store ground
water and also transmit it slowly from one aquifer to another.

ARTESIAN WELL - A  well deriving its water from a confined aquifer in which the water level in the casing
stands above the top of the confined aquifer.

BASALT - A general term for dark-colored iron- and magnesium-rich igneous rocks, commonly extrusive, but
locally intrusive.  It is the principal rock type making up the ocean floor.

BEDROCK - A general term for the rock, usually solid, that underlies soil or other unconsolidated material.

BIOFIXATION - The binding of radionuclides to the soil/organic matrix due to the action of some types of
microorganisms and plants, thus affecting mobility of the radionuclide.

BULK DENSITY - The  mass or weight of oven-dry soil per unit bulk volume, including air space.

CALIBRATION - The process by which a set of values for aquifer parameters and stresses is found that
approximates field-measured heads and flows. It is performed by trial-and-error adjustment of parameters and
boundary conditions or by using an automated parameter estimation code.

CAPTURE ZONE - The portion of the flow system that contributes water to a well or a surface water body such
as a river, ditch, or lake.
                                                 A-2

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CHAIN DECAY - Form of radioactive decay in which several daughter products may be produced before the
parent species decays to a stable element.

CLAY - (Clay particles are mineral particles < 0.002 mm. in diameter). In the grading of soils by texture, clay is
the extreme of fineness.

CONFINED AQUIFER - An aquifer which is overlain by a unit of porous material that retards the movement of
water.

CURVILINEAR ELEMENTS - Specialized elements used by finite-element computer codes that can be spatially
deformed to mimic the elevations of the upper and lower surfaces of the hydrogeologic units.

DARCY'S LAW - A derived equation that can be used to compute the quantity of water flowing through an
aquifer assuming that the flow is laminar and inertia can be neglected.

DETERMINISTIC MODEL - A model whose output is fixed by the mathematical form of its equations and the
selection of a single value for each input parameter.

DIP - The angle to the horizontal (slope) that a geologic unit may have.

DISCHARGE - The volume of water flowing in a stream or through an aquifer past a specific point in a given
period of time.

DISPERSION - A mixing phenomenon linked primarily to the heterogeneity of the microscopic velocities inside
the porous medium.

DISTRIBUTION COEFFICIENT - The slope of a linear Freundlich isotherm.

EFFECTIVE POROSITY - The volume of the void spaces through which water or other fluids can travel in a
rock or sediment divided by the total volume of the rock or sediment.

FACILITATIVE TRANSPORT - A term used to describe the mechanism by which radionuclides may couple
with either naturally occurring material or other contaminants and move at much faster rates than would be
predicted by their respective distribution coefficients.

FAULT - A fracture or a zone of fractures along which there has been displacement of the sides relative to one
another parallel to the fracture.

FINITE DIFFERENCE - A particular kind of a digital computer model based upon a rectangular grid that sets
the boundaries of the model and the nodes where the model will be solved.

FINITE ELEMENT - A digital ground-water flow model where the aquifer is divided into a mesh formed of a
number of polygonal cells.

FLOCCULATION - The agglomeration of finely divided suspended solids into larger, usually gelatinous,
particles; the development of a "floe" after treatment with a coagulant by gentle stirring or mixing.

FRACTURED LITHOLOGY - Porous media which is dissected by fractures.

FREUNDLICH ISOTHERM - An empirical equation that describes the amount of solute adsorbed onto a soil
surface.


                                                A-3

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GEOCHEMICAL FACIES - A unit of material of similar physical properties that was deposited in the same
geologic environment.

GROUT CURTAIN - An underground wall designed to stop ground-water flow; can be created by injecting grout
into the ground, which subsequently hardens to become impermeable.

GROUTING - The operation by which grout is placed between the casing and the sides of the well bore to a
predetermined height above the bottom of the well.  This secures the casing in place and excludes water and other
fluids from the well bore.

HETEROGENOUS - Pertaining to a substance having different characteristics in different locations.

HYDRAULIC CONDUCTIVITY - A coefficient of proportionality describing the rate at which water can move
through a permeable medium. The density and kinematic viscosity of the water must be considered in determining
hydraulic conductivity. The rate of flow of water in unit volume per unit of time through a unit cross section of
area of geologic material under a unit hydraulic gradient, at the prevailing temperature.

HYDRAULIC GRADIENT - The change in total head with a change in distance in a given direction. The
direction is that which yields a maximum rate of decrease in head.

HYDRODYNAMIC DISPERSION -  The process by which ground water containing a solute is diluted with
uncontaminated ground water as it moves through an aquifer.

HYDROFRACTURING - The process in which fluid is added to an aquifer at sufficient pressures to where the
pore pressure in the rock causes the rocks to fracture.

HYDROSTATIGRAPHIC UNIT - A formation, part of a formation, or group of formations in which there are
similar hydrologic characteristics allowing for grouping into aquifers or confining layers.

HYSTERESIS - A term which describes the fact that wetting and drying curves for a certain soil (pressure head
versus volumetric water content) under partially saturated conditions, are not the same.

IMMISCIBLE - Substances that do not mix or combine readily.

IN-SITU VITRIFICATION - Process by which electrodes are used to heat the soil-waste matrix to temperatures
high enough to melt soils and destroy organics by pyrolysis.

INTRINSIC PERMEABILITY - Pertaining to the relative ease with which a porous medium can transmit a
liquid under a hydraulic  or potential gradient.  It is a property of the porous medium and is independent of the
nature of the liquid or the potential field.

INVERSE MODEL - The model in which values of the parameters and the hydrologic stresses are determined
from the information about heads.

ION EXCHANGE - A process by which an ion in a mineral lattice is replaced by another ion that was present in
an aqueous solution.

LANGMUIR ISOTHERM - An empirical equation that describes the amount of solute adsorbed onto a soil
surface.

LAYERED  LITHOLOGY - Interbedded geologic units (e.g.,  sand, clay, gravel).


                                                A-4

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LEACH - The removal of soluble chemical elements or compounds by the passage of water through the soil.

LEACHATE - Water that contains a high amount of dissolved solids and is created by liquid seeping from a
landfill.

LIMESTONE - A sedimentary rock consisting chiefly of calcium carbonate, primarily in the form of the mineral
calcite.

LITTORAL - Pertaining to the ocean environment between the high tide and the low tide.

LOADING RATES - The rate at which contaminants and/or water enters the model domain.

LOW PERMEABILITY BARRIERS - Vertical or horizontal obstructions that are of sufficiently low
permeability to retard significantly the migration of water and/or contaminants.

MACROPORES - Large or noncapillary pores.  The pores, or voids, in a soil from which water usually drains by
gravity. Is differentiated from a micropore, or capillary pore space, which consists  of voids small enough that
water is held against gravity by capillarity.  Sandy soils have a large macropore, or noncapillary pore space and a
small micropore,  or capillary, pore space. Non-granular clayey soils are just the reverse.

MATRIX DIFFUSION - The diffusion of radionuclides from water moving within fractures, or coarse-grained
material, into the rock matrix or finer grained clays.

METAMORPHIC ROCK - Any rock  derived from preexisting rocks by mineralogical, chemical, and/or
structural changes, essentially in the solid state, in response to marked changes in temperature, pressure, shearing
stress, and chemical  environment, generally at depth in the Earth's crust.

MOLECULAR DIFFUSION - Dispersion of a chemical caused by the kinetic activity of the ionic or molecular
constituents.

NON-AQUEOUS PHASE LIQUIDS (NAPL) - Liquids that are immiscible in water.

NUMERICAL MODEL - One of five methods (finite-difference, finite element, integrated finite difference,
boundary integral equation method, and analytical elements) used to approximate by means of algebraic equations
the solution of the partial differential equations (governing  equation, boundary, and initial conditions) that
comprise the mathematical model. Numerical models can be used to describe flow  under complex boundary
conditions and where aquifer parameters vary within the model area.

ORGANIC COMPLEXATION - The  formation of organic complexes by the combination of organic material or
radionuclides.

PARTICLE TRACK - The movement of infinitely small imaginary particles placed in the flow field.

PARTITIONING -  The process by which a contaminant, which was originally in solution, becomes distributed
between the solution and the solid phase.

PERCHED WATER - Unconfined ground water separated from an underlying main body of ground water by an
unsaturated zone.

POROUS MEDIA - Rocks that are not dissected by discrete features (e.g., macropores, fractures).
                                                 A-5

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PROPRIETARY - A code in which the ownership rights are held by a company or organization.

RADIAL FLOW - The flow of water in an aquifer toward a vertically oriented well.

RADIOACTIVE DECAY - The change of a nucleus into another nucleus (or a more stable form of the same
nucleus) by the loss of a small particle or a gamma ray photon.

RECHARGE - The addition of water to the zone of saturation; also, the amount of water added.

RETARDATION FACTOR/COEFFICIENT - A measure of the capability of adsorption within the porous
media to impede the movement of a particular radionuclide being carried by the fluid.

SANDSTONE - A sedimentary rock composed of abundant rounded or angular fragments of sand set in a fine-
grained matrix (silt or clay) and more or less firmly united by a cementing material.

SATURATED ZONE - The zone in which the voids in the rock or soil are filled with water at a pressure greater
than atmospheric.  The water table is the top of the saturated zone in an unconfined aquifer.

SECOND AY MINERALIZATION - Mineralization that occurred later than the rock enclosing it.

SEDIMENTARY ENVIRONMENT - An environment in which the rocks are formed by the accumulation and
cementation of mineral grains transported by wind, water, or ice to the site of deposition or chemically precipitated
at the site of deposition.

SHALE - A fine-grained sedimentary rock, formed by the consolidation of clay, silt, or mud. It is characterized by
finely laminated structure and is sufficiently indurated so that it will not fall apart on wetting.

SILT - Soil particles between 1/256 and 1/2 mm in diameter, smaller than sand and larger than clay.

SOLUTION FEATURES - An opening resulting from the decomposition of less soluble rocks by water
penetrating pre-existing interstices, followed by the removal  of the decomposition products.

SOURCE TERM - The quantity of radioactive material released to the biosphere, usually expressed as activity per
unit time.  Source terms should be characterized by the identification of specific radionuclides and their physical
and chemical forms.

SPECIATION - The chemical form of the radionuclide, which can influence its solubility and therefore its rate of
transport by limiting the maximum concentration of the element dissolved in the aqueous phase.
                                                A-6

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            APPENDIX B
GROUND-WATER MODELING RESOURCES
                B-l

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               ELECTRONIC MEDIA-BASED SOURCES OF ASSISTANCE
Bulletin Boards

Access to bulletin boards is made via modem either by direct dialing or through a communication system like TELNET
or TYMNET.  Access to most systems is controlled by the use of login protocols and passwords obtained from the
system operator. Examples of existing systems include:
Name:                  ORB-BBS
Purpose:            Information about ORD operations and software available through ORD
Maintained by:             U. S. Environmental Protection Agency
                   Office of Research and Development
                   Cincinnati, Ohio
                          Charles W. Gulon
                          (513) 569-7610 (1200-2400 bps)
                   (800) 258-9605 (1200-9600 bps)
                   (513) 569-7700 (1200-9600 bps)
                   (513)569-7272
Communication Parameters:      1200, 2400, 4800, 9600 - N-8-1
Hours/Cost:             24 hours/7 days - Free
System Operator:
Modem Phone(s):
                       CEAM
                   Supports the use of exposure assessment models, especially
                   those used to model the transport of agricultural chemicals.
                          U. S. EPA
                   Office of Research and Development
                   Athens, Georgia
                          David Disney
                          (706) 546-3402
                   (FTS) 250-3549
                          (706) 546-3590
                   (706)546-3136
Communication Parameters:      1200, 2400 - N-8-1
Hours/Cost:             24 hours/7 days - Free
Name:
Purpose:

Maintained by:
System Operator:
Modem Phone(s):

Voice Phone(s):
Name:
Purpose:

Maintained by:
System Operator:
Voice Phone(s):
                       CSMoS
                   The Center for Subsurface Modeling Support (CSMoS) provides ground-water modeling
                   software and services to public agencies and private companies throughout the nation.
                          U.S. Environmental Protection Agency
                   Center for Subsurface Modeling Support
                   R.S. Kerr Environmental Research Laboratory
                          Dr. David S. Burden
                          (405) 332-8800
Bulletin Boards (Continued)
                                               B-2

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Name:                  CLU-IN
Purpose:            Current events information for hazardous waste cleanup professionals,
                   innovative technologies, and access to databases.
Maintained by:             U. S. EPA
                   Office of Solid Waste and Emergency Response
                   Technology Innovation Office
                   Washington, D.C.
System Operator:           Dan Powell
Modem Phone(s):           (301)589-8366
Voice Phone(s):            (301) 589-8368
Communication Parameters:      1200, 2400 - N-8-1
Hours/Cost:             24 hours/7 days - Free
Name:                  USGS BBS
Purpose:            General information from USGS
Maintained by:              U. S. Geological Survey
System Operator:
Modem Phone(s):            (703)648-7127
                   (703) 648-4168
Voice Phone(s):             (703) 648-7000
Communication Parameters:
Hours/Cost:             CD-ROM conference is Free

Name:                  ESDD
Purpose:            Earth Science Data Directory - list of nationwide databases of earth
                   science data
Maintained by:              U. S. Geological Survey
                   Reston,  Virginia
System Operator:            Joe Kemper
Modem Phone(s):            (703)648-4100
                   (703) 648-4200
Voice Phone(s):             (703) 648-7112\
Communication Parameters:       300, 1200, 2400, 9600 - 7-M-l
Hours/Cost:             Free (call voice phone for ID number)
                                                B-3

-------
Networks

In order to join a network conference, you must have access to a computer system that is a node in that network.
Access to the network can then be made by subscribing to a LISTSERV or joining a newsgroup.  Subscribing to a
LISTSERV is accomplished using the e-mail facility of a local node. A simple mail message is sent, SUB name, where
name is one of the address names below. Mail from that network conference will then appear in the user's e-mailbox.
Unsubscribing is accomplished by sending the message UNSUB name.

In addition, if the remote system permits, the user can access the remote node of the network via software like file
transfer protocol (FTP). Within a system like ftp, the user has direct access to the remote node as if it were a local
computer, and in some cases, software on the remote system can be run and the results later transferred to the local
node.

To FTP a remote site, the user types ftp node from the local node where node is one of the address names below. In
most cases, the remote node will require a login name and password if the ftp process is successful. The login name
is  often anonymous and the password guest, although other login strings are often called for and can only be
determined by contacting the individual in charge of the remote system.
Name:
Network:
Purpose:
Access:
    AQUIFER@BACSATA
BITNET
Discussion group on various ground-water protection issues.
    LISTSERV
Expert Systems
Name:
Source:
System Requirements:
Cost:
    Integrated Model Evaluation System
    Environmental Protection Agency
Office of Solid Waste and Emergency Response
Versar, Inc.
Ecological Sciences and Analysis Division
9200 Runsey Road
Columbia, Maryland 21045
            MSDOS
    Not yet determined
Name:
Purpose:
Source:
Cost:
    GMSYS
Estimate leach rates from landfills
    ORD-BBS
    Free
                                                B-4

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       APPENDIX C
SOLUTION METHODOLOGY
           C-l

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                                             APPENDIX C
Solution Methodology

Every ground-water model  is based upon a set of
mathematical equations. Solution methodology refers
to the  strategy and techniques used to solve these
equations.  In ground-water modeling, the equations
are normally solved for head (water elevations in the
subsurface) and/or contaminant concentrations.

Mathematical methods developed to solve the ground-
water flow and transport equations can be broadly
classified  as   either  deterministic  or  stochastic.
Deterministic methods assume that a system or process
operates such that the occurrence of a given set of
events leads to a uniquely definable outcome, while
stochastic methods presuppose  the outcome to be
uncertain and are structured to  account for  this
uncertainty.

Most of the stochastic methods are not completely
stochastic in that they often utilize a  deterministic
representation  of  soil processes  and derive  their
stochastic nature from their representation of inputs
and/or spatial variation  of soil characteristics  and
resulting chemical movement. While the deterministic
approach results in a specific value of a soil variable
(e.g., solute concentration) at pre-specified points in
the domain,  the stochastic approach  provides the
probability (within a level of confidence) of a specific
value occurring at any point.

The development of stochastic methods for solving
ground-water flow is a relatively  recent endeavor that
has occurred as a result of the growing awareness of
the  importance  of  intrinsic  variability  of  the
hydrogeologic environment. Stochastic methods are
still primarily research tools; however, as computer
speeds continue to increase, stochastic methods will be
able to move further away from the research- oriented
community and more into mainstream management
applications.     The  more  widespread  use  of
deterministic methods suggests a more immediate need
for code-selection  guidance.  Therefore, this  section
focuses primarily on deterministic methods.

Deterministic  methods may be broadly classified as
either analytical or numerical.  Analytical methods
usually  involve approximate or  exact  solutions to
simplified forms of the differential equations for water
movement and solute transport.  Simple analytical
methods are based  on the  solution of  applicable
differential  equations  which  make  a  simplified
idealization of the field and give qualitative estimates
of the extent of contaminant transport.  Such models
are  simpler to  use than numerical  models and can
generally  be solved with  the  aid  of a calculator,
although computers are also used. Analytical models
are  restricted  to  simplified  representations  of the
physical situations and generally require only limited
site-specific input data.  They are useful for screening
sites and scoping the problem to determine data needs
or the applicability of more detailed numerical models.

Analytical  models  are   used  in   ground-water
investigations  to  solve  many  different kinds  of
problems.   For  example,  aquifer parameters are
obtained  from aquifer tests through  the use  of
analytical  models,  and  ground-water flow   and
contaminant transport rates can also be estimated with
the use of analytical models. To avoid confusion, only
analytical models designed to estimate ground-water
flow and radionuclide transport rates are discussed in
this section.

Numerical models provide solutions to the differential
equations  describing water  movement  and solute
transport  using numerical  methods such as  finite
differences and finite elements. Numerical methods
can account for complex geometry and heterogenous
media, as  well as  dispersion, diffusion, and chemical
retardation processes (e.g.,  sorption,  precipitation,
radioactive decay, ion exchange, degradation). These
methods always require a  digital computer, greater
quantities of data than analytical modeling, and an
experienced modeler-hydrogeologist.

The  validity of the  results from numerical models
depends strongly  on the quality and quantity of the
input data. Numerical and analytical codes have their
respective  strengths  and  weaknesses  which  are
inherent within their formulations. The fundamental
characteristics  of both  analytical  and  numerical
methods are presented below and are discussed in more
detail in the following sections:
                                                   C-2

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Analytical
Analytical Methods
     !   Provides a solution at any location and point
        in time;

     !   Exact,  closed-form  solutions   or  well-
        documented,   convergent   solutions
        (approximate analytical);

     !   Requires regular geometry of the domain;

     !   Generally   requires    uniform   material
        properties;

     !   1-, 2-, or 3-D capability;

     !   Transient effects can be considered;

     !   Less  prone  to computational  errors than
        numerical methods;

     !   Usually requires that problems are linear;

     !   Low computer storage requirements;

     !   Data can be easily input.

Numerical

     !   Provides a  solution  only at prespecified
        locations and moments in time;

     !   Approximate solutions;

     !   Irregular domain  and boundaries can be
        simulated;

     !   Nonuniform  material  properties  can  be
        simulated;

     !   Can simulate non-linear problems;

     !   1-, 2-, or 3-D capability;

     !   Transient effects can be considered;

     !   Computational errors can be a problem;

     !   Can require large computer storage;

     !   Large amount of data input.
Analytical methods that solve ground-water flow and
contaminant   transport   in   porous  media  are
comparatively easy to use.   However, because the
governing equations are relatively simple, analytical
solutions are generally restricted to either radial flow
problems or to cases where velocity is uniform over the
area of interest. Except for some radial flow problems,
almost all  available  analytical solutions belong to
systems having a  uniform and steady flow.  This
means that the magnitude and direction of the velocity
throughout the system are invariable with respect to
time and  space, which  requires  the system to be
homogeneous and isotropic  with respect  to the
hydraulic conductivity. The three most general types
of analytical methods include the following:

     !   Approximate analytical

     !   Exact analytical

     !   Semi-analytical

Typical  analytical solutions,  which  are  termed
approximate, are in the form of an infinite series of
algebraic terms, or a double infinite series, or even an
infinite series of definite integrals. Because an infinite
series of numbers cannot be solved for exact solutions,
each one of these expressions must be approximated by
truncating the series after considering a predetermined
number of terms. If, on the other hand, the analytical
solution can be expressed by equations which take a
closed form (finite number of terms), the solution is
said to be exact. Even though the solution may contain
errors due to rounding.

In general,  exact analytical equations tend to require
infinite domains and boundaries.  These  constraints
typically result in solutions that are more appropriate
for  solving problems  of  well hydraulics  than those
associated with ground-water flow and contaminant
transport.

An obvious  problem with  approximate  analytical
equations is that they are of an open form and may not
converge if they are inherently unstable.  Therefore, it
is very important that care has been taken during the
code development process to ensure that the equations
used  do  converge  properly   and that  the  code
documentation provides  the  methods by which the
convergence was examined.   It is also important to
                                                   C-3

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recognize that just because a code is written using
analytical  techniques   it  does  not  mean  that
convergence may not still be  a problem even if the
formulation is correct.

Semi-analytical  methods are more  complex  than
analytical methods  and more simplistic than most
numerical methods. These techniques use the concepts
from fluid mechanics and velocity potentials which are
extended using numerical tools to construct flow and
contaminant patterns. Advantages of semi-analytical
methods include the following:

     !   Require only simple computer input data and
        do not require  the design of a mesh as with
        fully numerical methods;

     !   May be used where complex boundaries (e.g.,
        multiple  pumping  wells)  do  not  allow
        analytical equations to be written;

     !   Techniques can be used to easily estimate
        travel times of a conservative, retarded,  or
        decaying contaminant to a downgradient
        receptor;

     !   Can provide screening information to judge
        the need for more sophisticated modeling.

Limitations of semi-analytical methods include the
following:

     !   Mass transport by dispersion and diffusion is
        generally not  considered, which  in  many
        cases may lead to predictions of travel times
        that  are longer than actual values  and may
        underestimate   the  true  impact  of   a
        contaminant source;

     !   Usually are formulated in two dimensions and
        three-dimensional effects are  ignored;

     !   Heterogeneous properties of the media cannot
        be simulated although some semi-analytical
        methods do allow for anisotropy;

     !   Most semi-analytical formulations are for
        steady-state problems; however, in some cases
        they can be extended to handle  transient
        problems.

Numerical Methods
Unfortunately, the equations of flow and continuity in
the form of partial differential equations do not lend
themselves easily to rigorous analytical solutions when
boundaries are complex.   Therefore, if a realistic
expression for hydraulic head or concentration as a
function of space cannot be written from the governing
equations,  boundary  and  initial conditions,  then
analytical methods are generally abandoned and more
approximate numerical methods are used to solve the
set of equations.  The most common of these methods
include the following:

     !   Finite Difference

     !   Integrated Finite Difference

     !   Finite Element

     !   Method of Characteristics

Of particular importance to the following discussion is
the  understanding  that the flow  and transport
equations, which describe the movement of ground
water and contaminants, are  composed of both spatial
and  temporal  terms  both  of   which  require
discretization within the model domain. These terms
simply describe the concentration or head (i.e., water
elevations) in space and time. The numerical methods
mentioned  above  (i.e., finite element  and  finite
difference) are used as discretization methods for the
spatial term, whereas the  time-stepping methods,
discussed later in this section, are used to discretize or
describe the temporal term.

Finite Difference

The  basic  idea  of  finite-difference  methods is  to
replace derivatives at a point by ratios of the changes
in appropriate variables over small but finite intervals.
Unlike  analytical methods, where  values  can be
calculated  at  any point in the problem domain,
numerical  methods (e.g.,  finite  differences)  make
approximations at a predetermined finite number of
points  and reduce  a  continuous  boundary-value
problem to a set  of algebraic equations.  Once the
partial  differential equations have been converted into
a set of algebraic equations involving a number of
unknowns, the unknowns may be found by what are
termed matrix solvers.

In practice, the problem domain is  divided into  a
rectangular  grid  in  which  either  the x  and  y
                                                  C-4

-------
intersections, called nodes, are designated as solution
points (i.e., mesh centered) or the solution points are
at the center of the grid  cell (i.e., block centered).
Time step sizes are specified over the simulated time
of interest,  and the mathematical expressions are
successively solved for each individual time step until
the solution converges upon a value which satisfies the
predesignated  convergence  criteria  (i.e.,   error
tolerance).

The form of the system of equations is that the values
of head at each nodal point are a function of x and y
grid coordinates, as well as the size of specified time
steps. The values of head are related to the values in
the surrounding   nodal points  and those  at the
beginning and at the end of a time step. If the values
at the beginning of a time step are known  (which is
usually the case), the values at the end of the time step
are the  unknowns, and  the resulting  system  of
equations is a system of N  linear equations with N
unknowns. The value N indicates the total number of
mesh points. Thus, the mathematical problem to be
solved is the solution of a  linear system of equations.

The system of equations  may turn out to  be  rather
large. For example, a grid with 50  mesh points in the
x-direction and 50 mesh points in the y-direction will
have  2,500 unknowns  as well as equations  to be
solved.

Relevant considerations related to the finite-difference
method include:

     !   Uses a direct Taylor Series approximation of
        the derivative terms of the partial differential
        equations at nodal points;

     !   Formulation is based on a rectangular (block-
        centered or mesh-centered) grid;

     !   Relatively simple  to formulate as compared to
        other numerical methods;

     !   Conducive  to   efficient  matrix  solving
        techniques;

     !   May be sensitive to grid orientation effects in
        solving 2-D  and 3-D flow and  transport
        problems;
     !   Use of rectangular grid necessitates staircase
        (or stepwise)  approximation  of irregular
        boundary and/or aquifer material zoning;

     !   May be  prone to numerical dispersion or
        oscillation in solving transport problems.

A closely related alternative to the conventional finite
difference is the integrated finite-difference method
which uses integral approximations of the partial
differential equations  of  nodal subdomains.    The
primary advantage of  this  method is that it  will
accommodate non-rectangular grid elements, which
allow irregular boundaries to be efficiently modeled.
The  following,  however,  are the  disadvantages
associated with this method:

     !   Necessitates more complex grid generation
        scheme than the traditional finite-difference
        method;

     !   Subdomain    boundaries   surrounding
        individual   nodes   must   satisfy   certain
        orthogonality constraints to ensure that mass
        is conserved;

     !   Method leads to less efficient matrix solution
        techniques than  the  conventional finite-
        difference method.
                       ft^fl^ t .•CMtJf U£rt"£rtlf»
Figure C. 1   Finite Two-Dimensional Elements
Finite Element

While  approximations to a continuous solution are
defined at isolated points by finite differences, with
finite elements, the approximate solution (i.e., heads or
                                                   C-5

-------
concentration) is defined over the entire domain by
interpolation functions,  although solutions  to  the
functions are calculated only at the  element nodes.
This integral formulation for the governing ground-
water flow or solute transport equation leads to  a
system of algebraic equations that can be solved for the
unknown(s) (i.e., hydraulic head,  pressure head  or
solute concentration) at each node in the mesh. The
method of weighted residuals is the commonly used
general approach that defines an approximate solution
to the boundary or initial value problem. When this
approximate solution is substituted into the governing
differential equation,  an  error or residual occurs at
each point  (node)  in the  problem  domain.  The
weighted average of the residuals for each node in the
finite-element mesh is then forced to equal zero, thus
minimizing the error between  the  approxi-mate
solution  and  the  actual  solution.      Relevant
characteristics  of  the finite-element  method  as
compared with the finite-difference method include:

     !   Allows a much greater flexibility in handling
        irregular   domain  geometry,   material
        heterogeneity, and/or anisotropy;

     !   Less prone to numerical dispersion; however,
        it  is necessary to  be  more careful to limit
        potential oscillation in solving the  transport
        problem;

     !   The elements do not have to be rectangular,
        but  can also be  other  simple polygons
        (commonly triangles or quadrilaterals);

     !   Matrix    solutions    generally    require
        substantially greater computational effort and
        computer storage capability;

     !   Finite-element solutions are less sensitive to
        grid orientation.

Two typical problems that arise when solving the
contaminant  transport  equations  are  numerical
dispersion  and  artificial  oscillation.    Numerical
dispersion arises from grid size, time-step size,  and the
fact that computers have a limited accuracy, thus some
of the round-off error will occur in computations. This
error results in the artificial spreading of contaminant
due to  amplification of dispersivity.   Hence,  the
contaminant will disperse farther than it should with
a given physical, or "real" dispersivity.  This extra
dispersion will result in lower peak concentrations and
more spreading of the contaminant. Methods exist to
control  numerical   dispersion,  but  the  methods
themselves  may  introduce  artificial   oscillation.
Artificial oscillation is the over or undershooting of the
true  solution by the model, and results in "waves" in
the  solution.    Usually  numerical  dispersion is
associated with the finite-difference method; however,
numerical oscillation is  associated with the finite-
element  method.    Depending upon the  method
employed to solve the advection term, both methods
can exhibit both types of behavior. Special techniques
have been developed to deal with these problems, one
of which is the Method of Characteristics  (MOC).

This method has been widely used and can be applied
to finite differences as well as finite elements, in two or
three dimensions.  The basic idea is to decouple the
advective part and the dispersive part of the transport
equation and to solve them successively. However, all
MOC methods are not strictly based on the  principle of
mass conservation,  hence  large contaminant mass
balance errors may arise. While it is recognized that
these errors may be  an artifact of the technique, the
quality of the results of a numerical model are judged,
in part,  by  the  degree  that  mass  is  conserved.
Furthermore,  the  MOC technique  requires  much
longer run-times  than finite-difference  or finite-
element techniques.	
           -----— r
Figure C-2.   Three-Dimensional Elements
                                                   C-6

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Time Stepping

As  mentioned previously, while  finite-element and
finite-difference methods are used to approximate the
spatial terms  of the transient flow  and transport
equations, techniques are used to approximate  the
temporal term.  While there are  several commonly
used variations of the finite-difference method, it is
beyond the scope of this discussion to elaborate on the
specifics for each of the techniques; what is important,
however, is an introduction to the technical terms and
a general understanding as to how the various methods
influence the model run-times as well as the results.
Four  of the  most common time-stepping schemes
include Explicit, Implicit, Mixed Explicit-Implicit, and
Alternating  Direction   Implicit  Procedure.
Characteristics of each method are listed below.

Explicit:

     !   Numerical solution is conditionally stable.

     !   Often requires an excessive number of time
        steps to simulate a practical problem.

     !   Due to numerical inefficiencies, method is
        unsuitable for simulation of field problems
        with a high degree of heterogeneity and/or
        nonlinear flow conditions.

Implicit:

     !   Usually  produces  unconditionally  stable
        numerical solution for flow and transport.

     !   Much more  flexible and  robust than  the
        explicit time-stepping scheme.

     !   Matrix  formulation and solution  require
        substantial  computational   effort  (i.e.,
        relatively long computer times are necessary
        to model practical field problems).

Mixed Explicit-Implicit:

     !   Based on combined use  of explicit and
        implicit temporal approximations.

     !   Usually  produces  unconditionally  stable
        numerical solution for flow and transport.
     !   More robust than the explicit time-stepping
        scheme, and generally more efficient than the
        implicit scheme for ground-water flow and
        transport solutions.

     !   Time-stepping  scheme can be weighted in
        favor of  either method  (i.e.,  explicit  or
        implicit) using a factor that ranges from 0 to
        1. Weighting factors of 0, .5, and 1 result in
        explicit, Crank-Nicholson, and fully implicit
        formulations, respectively.

Alternating Direction Implicit Procedure:

     !   Usually  produces  unconditionally  stable
        numerical solution for flow and transport.

     !   Much more flexible and robust than  the
        explicit time-stepping scheme.

     !   May be prone to mass balance problems when
        applied to field problems with high degree of
        heterogeneity   and/or  nonlinear   flow
        conditions.

     !   Unsuitable  for variably  saturated  flow
        simulations.
     I
        Limited to rectangular finite-difference grids.
The end result of applying the time-stepping schemes
described above is that the flow and transport problem
is  broken  into  multiple equations with  multiple
unknowns for each pre-specified point in the model
domain (i.e., nodes). These multiple equa-tions will,
in turn, be solved through matrix algebra methods
which are discussed in a later section.

Linearization of Flow and Transport Equations

In earlier sections, several situations were presented in
which the equations describing ground-water flow and
contaminant transport are nonlinear.  For transport
problems, the equations are nonlinear when changes in
concentration,  pressure,  and temperature   cause
changes in viscosity, effective porosity, ordensity (e.g.,
multiphase fluid conditions). Nonlinearflow problems
involve those where the transmissivity is a function of
saturated thickness  (i.e., water-table  aquifers)  or
hydraulic conductivity is a function of moisture content
(i.e., unsaturated zone).
                                                   C-7

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Under nonlinear flow and transport conditions each
node  in the model domain has associated multiple
nonlinear equations. Priorto solving for the unknowns
of  these  equations  through matrix  algebra,  an
intermediate step is required in which the  equations
are linearized. Two of the most common procedures
used to perform this linearization are the Picard and
Newton-Raphson methods.

The Picard method:

     !   Is relatively simple to formulate as compared
        to the Newton-Raphson procedure.
     I
        Generally produces a symmetric matrix for
        the  flow   problem  and  thus  requires
        considerably less  computer effort for  the
        matrix solution  than the  Newton-Raphson
        method.
     !   May be prone to convergence difficulties for
        highly nonlinear cases.

Qualities of the Newton-Raphson method include:

     !   Suitable for handling highly nonlinear cases.

     !   Generally  requires   substantially  greater
        computational effort for matrix formulation
        and solution.

     !   Convergence of the procedure may depend on
        continuity or smoothness of the nonlinear
        functions.

As far as model selection is concerned, if it is expected
that the problem will be highly nonlinear, the code
selected should be able to apply the Newton-Raphson
method.  It should also  be recognized that in this
situation the calculations will take a relatively long
time for the computer to solve.  Flow and transport
through the unsaturated zone become more nonlinear
as the contrast between ambient moisture content and
volume of recharge (e.g., rainfall)  becomes  more
pronounced.   Therefore,  the  regional climate can
provide an  indication as to whether unsaturated zone
flow and transport are likely to be nonlinear or highly
nonlinear.  For example, high-intensity rainfall events
in the arid southwest would create very sharp contrasts
between the  ambient  moisture  content and  the
infiltrating pulse.  Under these conditions, the code
would   most   likely  need  the   Newton-Raphson
formulation.   However,  in areas  of the humid
northeast, the ambient moisture contents are generally
high enough that the wetting front saturations are not
significantly  different  from  the  ambient  moisture
content and therefore the nonlinear equations could be
adequately solved with the Picard method.

Matrix Solvers

As  stated  previously,  following the  spatial  and
temporal discretization of the flow  and transport
equations and in the case of nonlinear problems, the
linearization  of  the  equations,  it  then  becomes
necessary to solve the systems of multiple equations
with multiple unknowns. The most efficient means of
accomplishing this  task is through matrix algebra.
Matrix equations can be  solved by  several means.
Some of the more common ones include:

     !   Direct Matrix Solution Techniques

     !   Iterative Alternating Direction Implicit
        Procedure (IADIP)

     !   Successive Over-Relaxation Techniques

     !   Strong Implicit Procedure (SIP)

     !   Preconditioned Conjugate Gradient
        (PCG)/Orthomin Techniques

It  is  important  to recognize that matrix solving
techniques will rarely be the deciding factor in the
code selection process.  However, some familiarity
with the capabilities of the matrix solvers will not only
provide a general recognition of the technical terms
but will  also give some indication as to   potential
hardware requirements.   Therefore,  the following
provides a superficial description of the various matrix
solvers listed  above.

The following qualities are inherent in the Direct
Matrix Solution techniques:

     !   Produces  highly  accurate  solution of the
        matrix equation  with  minimal  round-off
        errors.

     !   Generally applicable to both finite-difference
        and finite-element schemes.

-------
     !   Performs well for 2-D problems with up to
        2,000 nodal unknowns; unsuitable for large
        problems with many thousands of nodes.

Qualities of the Iterative Alternating Direction Implicit
Procedure (IADIP) include:

     !   Accommodates large 2-D and 3-D problems
        with many thousands of nodal unknowns.

     !   Applicability  limited to rectangular grids.

     !   Convergence  rate is usually sensitive to grid
        spacings  and material  heterogeneity and
        anisotropy.

     !   Prone to asymptotic convergence behavior
        and  may  require  several   hundreds  or
        thousands of  iterations to reach satisfactory
        convergence for a steady-state analysis.

Qualities  inherent  in Successive Over-Relaxation
Techniques (i.e., Point Successive Over-Relaxation
(PSOR), Line Successive Over-Relaxation (LSOR),
and  Slice  Successive   Over-Relaxation  (SSOR))
include:
     !   Convergence rate  is sensitive to iteration
        parameter and grid spacings.

     !   Applicable to finite-difference approximation
        and flow problems only.

Qualities inherent  in the Preconditioned  Conjugate
Gradient (PCG)/Orthomin Techniques include:

     !   Accommodates large 2-D and 3-D problems
        with many thousands of nodal unknowns.

     !   No relaxation factor or iteration parameters
        are required and convergence rate is usually
        insensitive to  grid spacings  and material
        anisotropy and/or heterogeneity.

     !   Much more robust than other  alternative
        iteration techniques.
     I
        Applicable to  both finite-difference  and
        finite-element  approximation schemes but
        requires   substantially   less  storage   and
        computer  (CPU) time with finite-difference
        approximation, particularly for 3 -D problems.
     !   Accommodates large 2-D and 3-D problems
        with many thousand nodal unknowns.

     !   Applicable  to finite-difference  and finite-
        element approximation schemes.

     !   Convergence rate is dependent on the choice
        of relaxation factors and is usually sensitive
        to grid spacings and material heterogeneities
        and anisotropies.

     !   Prone to asymptotic convergence behavior
        and  may  require several  hundreds  or
        thousands of iterations to reach satisfactory
        convergence for a steady-state analysis.

Qualities inherent in the  Strong  Implicit Procedure
(SIP) include:

     !   Accommodates large 2-D and 3-D problems
        with many thousand nodal unknowns.

     !   Much   more  robust  than  IADIP   and
        PSOR/LSOR/SSOR techniques.
                                                  C-9

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      APPENDIX D
CODE ATTRIBUTE TABLES
          D-l

-------
Site-Related Features of Ground Water Flow and Transport Codes
COMPUTER CODE



BOUNDARY/SOURCE
CHARACTERISTICS

| POINT SOURCE |




| LINE SOURCE |




| AREALLY DISTRIBUTED |




| SPECIFIED |




| SPECIFIED SOURCE RATE |




| TIME-DEPENDENT |




| MULTIPLE SOURCES |



AQUIFER SYSTEM
CHARACTERISTICS

| CONFINED AQUIFERS |




| AQUITARDS |




| WATER-TABLE |




| CONVERTIBLE AQUIFERS |




| MULTIPLE AQUIFERS |



SOIL/ROCK CHARACTERISTICS

| HOMOGENEOUS |




| HETEROGENEOUS |




| ISOTROPIC |




| ANISOTROPIC |




| FRACTURED |




| MACROPORES |




| LAYERED SOILS |



REFERENCE
CITATION



COMPUTER
CODE




TRANSPORT & FATE PROCESSES
-
• DISPERSION



-
• ADVECTION



-
• MATRIX DIFFUSION



—
• DENSITY-DEPENDENT



-
• RETARDATION



-
• NON-LIN. SORPTION



—
• CHEMICAL REACTIONS/



—
• SINGLE SPECIES



—
1 MULTI-SPECIES TRANS-
PORT WITH CHAINED



MULTIPHASE
FLUID CONDITIONS
• TWO-PHASE



| TWO-PHASE WATER/AIR



1 THREE-PHASE WATER/
NAPL/AIR



FLOW
CONDITION^^
| FULLY SATURATED



• VARIABLY SATURATED/
NON-HYSTERETIC



• VARIABLY SATURATED/



TIME
DEPENDENCE
| STEADY-STATE



| TRANSIENT




-------
Code-Related Features of Ground Water Flow and Transport Codes
COMPUTER CODE



SOLUTION METHODOLOGY
• APPROX. ANALYTICAL _ | ;>



1 g.
• EXACT ANALYTICAL | ^.



• SEMI-ANALYTICAL |



Numerical
• FINITE DIFFERENCE |£



• INTEGRATED FINITE- &
K2



1 *4
| FINITE ELEMENT ||



iOfc
• METHOD OF CHARAC.



sen zati
• EXPLICIT



• IMPLICIT



• MIXED IMPLICIT-



Mateg Solars

PH
3



• DIRECT SOLUTION



• ITERATIVE ADIP



• SOR/LSOR/SSOR




P_H
GO



• PCG/ORTHOMIN



GEOMETRY

Q



• 2-D CROSS SECTIONAL



• 2-DAREAL



• QUASI 3-D (LAYERED)



| FULLY 3-D



COMPUTER CODE



OTHER RELEVANT FACTORS
Source Code
^ailabili^
| PROPRIETARY



| NON-PROPRIETARY



Code Testing and
™ P™ess ™
| VERIFIED



| FIELD-VALIDATED



| PC- VERSION 386-SR486



| PRE AND POST



_
(CONTAMINANT MASS/
RATE OF RELEASE TO
GROUNDWATER FROM



• CONTAMINANT PLUME 1
EXTENT |



(CONTAMINANT 1
CONCENTRATION ASA 1
FUNCTION OF DISTANCE 1
ii r*,



• AS A FUNCTION OF 1 *f



• CONTINUOUSLY 1
DISTRIBUTED IN SPACE |



_ —
(CONTAMINATION
AVERAGE
AT SELECTED POINTS



• PROFILES AT SELECTED
POINTS OVER TIME




-------
APPENDIX E
   INDEX
    E-l

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                                                 INDEX
                                                         D
Adsorption  S-12, 3-3, 4-35, 4-37, 4-51, A-2, A-6
Advection S-9, S-12, S-13, S-16, 4-20, 4-25, 4-35,
  4-37, 4-38, 4-39, 4-40, 4-45, 5-4, 5-20, A-2, C-6,
  D-3
Alluvial flood plane  4-15
Analytical model 4-7, A-2
Anion exclusion 4-17, 4-41, A-2
Anisotropic S-7, S-9, S-10, S-ll, 4-2, 4-9, 4-25,
  4-28, 4-32, 5-7, A-2, D-3
Aquifer S-5, S-8, S-9, S-10, S-ll, S-12, S-16,
  1-3, 1-4, 3-5, 4-4, 4-9, 4-10, 4-12, 4-13, 4-16,
  4-18, 4-22, 4-24, 4-25, 4-27, 4-28, 4-29, 4-30,
  4-35, 4-36, 4-37, 4-38, 4-39, 4-45, 4-46, 4-47,
  4-49, 5-4, 5-8, 5-16, 5-20, 5-22, A-2, A-3, A-4,
  A-5, A-6, B-4, C-2, C-5, D-l
Aquitards S-10, S-ll, S-16, 4-10, 4-22, 4-28, 4-30,
  4-37, 4-45, 4-46, 5-4, 5-20, 5-22, D-2
Artesian well A-2
B
Basalt 3-4, A-2
Bedrock 4-15, A-2
Benchmark  S-15, 5-1, 5-2
Biofixation  4-17, 4-18, 4-41, A-2
Bulk density  A-2
Calibration  4-12, 4-16, 4-31, 4-32, 4-40, 4-47, A-2
Capture zone  S-13, 4-40, 4-43, A-2
Chain decay  S-17, 5-5, A-3
Channeling  4-37
Chemisorption S-13, 4-41
Clay S-13, 4-16, 4-17, 4-49, A-3, A-4, A-6
Complexation 3-3, 4-16, 4-17, 4-50, A-5
Concentration gradient S-13, 4-40
Conceptual model  S-l, S-5, S-6, S-8, S-12, 1-3,
  1-4, 1-5, 3-1, 3-2, 3-3, 3-5, 4-1, 4-3, 4-6,
  4-7, 4-10,  4-11, 4-12, 4-14, 4-21, 4-24, 4-31,
  4-32, 4-39, 4-47, 5-8, 5-15, 5-16
Convergence 4-15, 4-34, C-4, C-5, C-8, C-9
Curvilinear elements 4-37, A-3
Darcy's Law  4-30, 4-49, A-2, A-3
Deterministic model 4-47, 5-15, A-3
Dip  4-31, 4-36, A-3
Discharge  3-4, 3-5, 4-13,  4-31, 4-32, 4-43, 4-49,
  A-3
Dispersion S-6, S-9, S-10, S-12, S-13, S-16, 1-2,
  3-5, 4-13, 4-17, 4-20, 4-25, 4-27, 4-28, 4-32,
  4-35, 4-37, 4-38, 4-39, 4-40, 4-45, 5-4, 5-16,
  5-20, A-3, A-4, A-5, C-2, C-4, C-5, C-6, D-3
Distribution coefficient  S-13, S-14, 2-2, 4-9, 4-15,
  4-41, 4-42, 4-50, 5-8, A-3
Downgradient  S-2, S-3, 1-3, 2-1, 2-4, 3-5, 4-5,
  4-11, 4-12, 4-13, 4-19, 4-27, 4-43, 4-45,  5-20,
  C-4
E
Effective dose equivalent 2-6
Effective porosity  4-4, 4-30, A-3, C-7
Equilibrium isotherm S-17, 5-5
Exposure scenarios S-4, S-5, S-6, 2-4
Facilitative transport 4-5, 4-15, 4-48, 4-49, A-3
Fault 4-50, A-3
Finite difference 4-26, A-3, A-5, C-4, C-5, D-5
Finite element  4-26, A-3, A-5, C-4, C-6, D-5
Flocculation  4-16, A-3
Fractured lithology  A-3
Freundlich isotherm A-3
Geochemical facies 4-15, A-4
                                                   E-2

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H
M
Hydraulic gradient  S-13, 4-4, 4-17, 4-40, 4-49, A-4
Hydrodynamic dispersion S-12, S-13, 4-35, 4-37,
  4-39, A-4
Hydrofracturing 4-17, A-4
Hydrogeologic unit 4-50
Hydro statigraphic unit A-4
Hysteresis  4-44, A-4
I
Immiscible  S-14, 4-42, A-4, A-5
In-situ coating  4-16
In-situ freezing 4-16
Institutional control S-4, 2-4
Integrated finite difference A-5, C-4
Intrinsic permeability  S-ll, 4-32, A-4
Inverse model A-4
Ion exchange S-13, 4-18, 4-41, 4-49, 5-16, A-4, C-2
Ionic or molecular constituents  S-13, 4-40, A-5
Macropores S-9, S-10, S-ll, S-16, 4-5, 4-9, 4-15,
  4-22, 4-25, 4-28, 4-32, 4-33, 4-34, 4-35, 4-44,
  5-4, A-5, D-3
Matrix diffusion  S-9, S-12,  S-13, 4-14, 4-15, 4-18,
  4-20, 4-22, 4-25, 4-38, 4-39, 4-40, A-5, D-3
Mechanical dispersion S-13, 4-39
Metamorphic rock 4-36, A-5
Model S-l, S-2, S-5, S-6,  S-7, S-8, S-10, S-ll,
  S-12, S-13, S-14, S-15, S-16, S-18, S-19, S-20,
  1-2, 1-3, 1-4, 1-5, 2-7, 2-8, 3-1, 3-2, 3-3, 3-5,
  4-1, 4.3, 4.4, 4.5, 4-6, 4-7, 4-9, 4-10, 4-11, 4-12,
  4-13, 4-14, 4-15, 4-16, 4-20, 4-21, 4-22, 4-23,
  4-24, 4-26, 4-27, 4-28, 4-30, 4-31, 4-32, 4-37,
  4-38, 4-39, 4-40, 4-42, 4-43, 4-44, 4-45, 4-47,
  4-48, 4-50, 4-51, 5-1, 5-2, 5-4, 5-5, 5-7,  5-8,
  5-10, 5-13, 5-14, 5-15, 5-16, 5-20, A-2, A-3, A-4,
  A-5, B-2, B-4, C-2, C-4, C-6, C-7, C-8
Molecular diffusion  S-13, 4-35, 4-39, A-5
Monitor wells  S-4
Multiple aquifers S-9, S-10, S-ll, S-16, 4-16, 4-22,
  4-25, 4-28, 4-30, 5-4, D-2
Joint sets  4-36
K
Kinetic activity 4-40, A-5
Langmuir isotherm A-4
Layered lithology  A-4
Leach 1-3, 4-20, A-5, B-4
Leachate  S-2, S-10, 1-4, 2-1, 2-2, 4-28, 4-43, A-5
Limestone 3-4, 4-36, 4-49, A-5
Lithography  3-2, 4-7
Littoral A-5
Loading rates 4-43, A-5
Low permeability barriers S-12, 4-38, A-5
                                                         N
                                                         Numerical model  4-9, 4-11, 4-47, A-5, C-6
                                                         Numerical oscillations S-12, 4-39
O
Off-centerline dispersion modeling  3-5
One-dimensional S-8, 3-4, 4-2, 4-5, 4-6, 4-27, 4-45,
  5-20
Organic Complexation 4-17, A-5
Oxidation-reduction potential  4-16
Particle track A-5
Partition factors S-2, 2-2
Perched water 4-32, A-5
Porous media  S-12, 3-5, 4-4, 4-9, 4-14, 4-35, 4-36,
  4.39,  4.44, 5.7, A-3, A-5, A-6, C-3
Pyrophoric 4-31
                                                    E-3

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R
Radial flow 4-9, A-6, C-3
Radioactive decay S-ll, S-12, S-14, S-17, 3-3,
  4-12, 4-28, 4-37, 4-38, 4-41, 4-42, 5-5, 5-16, A-3,
  A-6, C-2
Receptors  S-5, S-6, 1-4, 2-6, 3-2, 3-5, 4-4, 4-5,
  4-11,4-12,4-19,4-27
Recharge 3-4, 3-5, 4-4, 4-5, 4-9, 4-13, 4-18, 4-19,
  4-20, 4-28, 4-29, 4-30, 4-31, 4-33, 4-34, 4-35,
  5-7, 5-22, A-6, C-8
Regional scale  3-4, 3-5
Remediation S-l, S-2, S-4, S-7, S-12, S-13, S-16,
  1-2,  1-3, 1-5, 2-1, 2-3, 2-6, 2-7, 3-1, 3-2, 4-1,
  4-2, 4-3, 4-7, 4-11, 4-21, 4-29, 4-30, 4-32, 4-38,
  4-40, 4-43, 5-4, 5-7
Retardation factor/coefficient A-6
Sandstone  S-ll, 4-9, 4-36, 4-37, A-6
Saturated zone S-ll, 3-4, 4-5, 4-6, 4-7, 4-10, 4-12,
  4-13, 4-19, 4-30, 4-31, 4-34, 4-35, 4-43, 4-44,
  4-48, 5-8, 5-20, A-6
Secondary  mineralization 4-16
Sedimentary environment A-6
Shale 3-4, A-6
Silt A-6
Solute S-12, S-13, 4-33, 4-37, 4-38, 4-39, 4-41,
  4-42, 4-47, 4-48, 5-8, 5-16, 5-20, A-2, A-3, A-4,
  C-2, C-6
Solution features  4-15, A-6
Source term  S-5, S-10, 3-2, 3-3, 4-12, 4-18, 4-24,
  4-27, 4-28, 4-43, 4-44, 4-45, 4-48, 4-50, 5-20,
  A-6
Speciation S-9, S-17, 4-17, 4-25, 4-41, 4-49, 5-5,
  A-6, D-4
Three-dimensional  S-8, 4-1, 4-7, 4-12, 4-13, 4-15,
  4-19, 4-27, 4-45, 4-46, 5-20, 5-22, C-4, C-6
Two-dimensional 4-2, 4-5, 4-6, 4-12, 4-13, 4-19,
  4.45, 4-46, 4-48, 5-16, 5-20, 5-22, C-5
                                                    E-4

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